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{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{\\log{\\left(x \\right)}}}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x e^{x}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x e^{x}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(x \\left(\\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)} + \\log{\\left(x \\right)} + 1\\right) e^{x \\log{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(\\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)} \\cos{\\left(x \\log{\\left(x \\right)} \\right)} + \\log{\\left(x \\right)} \\sin{\\left(x \\log{\\left(x \\right)} \\right)} + \\sin{\\left(x \\log{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(\\sin{\\left(x \\right)} \\cos{\\left(\\sin{\\left(x \\right)} \\right)} + \\sin{\\left(\\sin{\\left(x \\right)} \\right)}\\right) \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\left(x^{2} \\left(\\frac{x \\sin{\\left(2 x \\right)}}{2} - \\cos{\\left(2 x \\right)} + 1\\right) + 2 x \\cos{\\left(x \\right)} + 4 \\sin{\\left(x \\right)}\\right) e^{x^{2} \\sin{\\left(x \\right)}} \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\cos{\\left(x \\right)}, g(x) = x^{2} \\log{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Provide an integer within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\cos{\\left(x \\right)}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": "1", "correct_answer": "1", "answer_format": "integer"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "e^{x}", "x_value": null, "correct_answer": "e^{x} \\cos{\\left(e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{\\frac{x}{\\tan{\\left(x \\right)}} + 2}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x", "g": "e^{x}", "x_value": null, "correct_answer": "e^{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{3}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{3}", "x_value": null, "correct_answer": "3 x^{2} \\left(\\log{\\left(x^{3} \\right)} + 1\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "- x \\left(x \\cos{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right) \\sin{\\left(x^{2} \\sin{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{4}", "x_value": null, "correct_answer": "4 x^{3} \\left(\\log{\\left(x^{4} \\right)} + 1\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\left(\\log{\\left(\\cos{\\left(x \\right)} \\right)} + 1\\right) \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "e^{x}", "x_value": null, "correct_answer": "e^{x} \\cos{\\left(e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "e^{x}", "x_value": null, "correct_answer": "\\left(2 \\log{\\left(e^{x} \\right)} + 1\\right) e^{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(\\sin{\\left(x \\right)} \\cos{\\left(\\sin{\\left(x \\right)} \\right)} + \\sin{\\left(\\sin{\\left(x \\right)} \\right)}\\right) \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x", "x_value": null, "correct_answer": "x \\left(2 \\log{\\left(x \\right)} + 1\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{5}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{5}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{9} \\cdot \\left(10 \\log{\\left(x \\right)} + 5\\right) \\log{\\left(x \\right)}^{4}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x^{2} \\cos{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": "1", "correct_answer": "0.41", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = x \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "x \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "3 x^{2} \\left(- x \\sin{\\left(x \\right)} + \\cos{\\left(x \\right)}\\right) \\cos^{2}{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x e^{x}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x e^{x}", "x_value": "1", "correct_answer": "82.39", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = x \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\tan{\\left(x \\right)} + \\frac{1}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": "1", "correct_answer": "0.71", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{5}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{5}", "g": "e^{x}", "x_value": null, "correct_answer": "5 e^{5 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\left(\\log{\\left(\\cos{\\left(x \\right)} \\right)} + 1\\right) \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x e^{x}", "x_value": null, "correct_answer": "- \\left(x + 1\\right) e^{x} \\sin{\\left(x e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{4}, g(x) = \\sqrt{x}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Provide an integer within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{4}", "g": "\\sqrt{x}", "x_value": "1", "correct_answer": "2", "answer_format": "integer"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = \\sqrt{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "x_value": null, "correct_answer": "\\frac{e^{\\sqrt{x}}}{2 \\sqrt{x}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = \\sqrt{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "x_value": null, "correct_answer": "\\frac{e^{\\sqrt{x}}}{2 \\sqrt{x}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{\\log{\\left(\\log{\\left(x \\right)} \\right)} + 1}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{4}, g(x) = x^{3}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{4}", "g": "x^{3}", "x_value": null, "correct_answer": "12 x^{11}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\cos{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\cos{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{- \\log{\\left(x \\right)} \\sin{\\left(\\log{\\left(x \\right)} \\right)} + \\cos{\\left(\\log{\\left(x \\right)} \\right)}}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(2 \\log{\\left(x \\right)} + 1\\right) e^{x^{2} \\log{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = x^{2} e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "x^{2} e^{x}", "x_value": null, "correct_answer": "\\frac{3 \\left(x^{2} e^{x}\\right)^{\\frac{3}{2}} \\left(x + 2\\right)}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- 3 \\sin{\\left(x \\right)} \\cos^{2}{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = \\sin{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "\\sin{\\left(x \\right)}", "x_value": "1", "correct_answer": "3.00", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{x}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(- x \\log{\\left(x^{2} \\cos{\\left(x \\right)} \\right)} \\sin{\\left(x \\right)} - x \\sin{\\left(x \\right)} + 2 \\log{\\left(x^{2} \\cos{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} + 2 \\cos{\\left(x \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x^{\\frac{5}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x^{\\frac{5}{2}}", "x_value": null, "correct_answer": "\\frac{5 x^{\\frac{3}{2}} e^{x^{\\frac{5}{2}}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{4}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{4}", "g": "x^{4}", "x_value": null, "correct_answer": "16 x^{15}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = \\sqrt{x}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "\\sqrt{x}", "x_value": "1", "correct_answer": "4.08", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\cos{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\cos{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(- \\sin{\\left(x \\right)} \\sin{\\left(\\sin{\\left(x \\right)} \\right)} + \\cos{\\left(\\sin{\\left(x \\right)} \\right)}\\right) \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{\\sqrt{x \\log{\\left(x \\right)}} \\left(\\log{\\left(x \\right)} + 1\\right)}{2 x \\log{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "3 \\sin^{2}{\\left(x \\right)} \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x^{3}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{3}", "x_value": "1", "correct_answer": "1.62", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{1}{\\tan{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\cos{\\left(x \\right)}, g(x) = x^{2} e^{x}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\cos{\\left(x \\right)}", "g": "x^{2} e^{x}", "x_value": "1", "correct_answer": "-65.17", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = x^{\\frac{5}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{\\frac{5}{2}}", "x_value": null, "correct_answer": "\\frac{5}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = x \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "x \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "3 x^{2} \\left(- x \\sin{\\left(x \\right)} + \\cos{\\left(x \\right)}\\right) \\cos^{2}{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\log{\\left(x \\right)} \\log{\\left(x \\log{\\left(x \\right)} \\right)} + \\log{\\left(x \\right)} + \\log{\\left(x \\log{\\left(x \\right)} \\right)} + 1", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{1}{\\tan{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{5}{2}}, g(x) = x \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{5}{2}}", "g": "x \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{5 \\left(x \\cos{\\left(x \\right)}\\right)^{\\frac{5}{2}} \\left(- x \\tan{\\left(x \\right)} + 1\\right)}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{5}{2}}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{5}{2}}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\frac{5 \\sin{\\left(x \\right)} \\cos^{\\frac{3}{2}}{\\left(x \\right)}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = e^{x}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "e^{x}", "x_value": "1", "correct_answer": "22.17", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "- x \\left(x \\cos{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right) \\sin{\\left(x^{2} \\sin{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "\\sin{\\left(x \\right)} \\sin{\\left(\\cos{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\frac{3 \\sin{\\left(x \\right)} \\sqrt{\\cos{\\left(x \\right)}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{5}{2}}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{5}{2}}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{5 \\left(x^{2} \\cos{\\left(x \\right)}\\right)^{\\frac{5}{2}} \\left(- x \\tan{\\left(x \\right)} + 2\\right)}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{\\sin{\\left(x \\right)}} \\cos{\\left(x \\right)}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\cos{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\cos{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{\\left(- \\log{\\left(x \\right)} \\sin{\\left(\\log{\\left(x \\right)} \\right)} + 2 \\cos{\\left(\\log{\\left(x \\right)} \\right)}\\right) \\log{\\left(x \\right)}}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\cdot \\left(2 x \\log{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} + x \\cos{\\left(x \\right)} + 4 \\log{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\sin{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right) \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x e^{x}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x e^{x}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(- x^{2} \\left(\\frac{x \\sin{\\left(2 x \\right)}}{2} - \\cos{\\left(2 x \\right)} - 1\\right) - x \\sin{\\left(x \\right)} + 2 \\cos{\\left(x \\right)}\\right) e^{x^{2} \\cos{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Solve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{3 \\log{\\left(x \\right)}^{2}}{x}", "answer_format": "latex"}}