prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{3}{2}}, g(x) = \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

g: \log{\left(x \right)}

correct_answer: \frac{3 \sqrt{\log{\left(x \right)}}}{2 x}

answer_format: latex


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x e^{x}, g(x) = x \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: x e^{x}

g: x \log{\left(x \right)}

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)}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \sin{\left(x \right)}, g(x) = x \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: x \sin{\left(x \right)}

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)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: x

g: \sin{\left(x \right)}

correct_answer: \cos{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \sin{\left(x \right)}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} e^{x}, g(x) = x^{2} \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

g: x^{2} \sin{\left(x \right)}

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)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \cos{\left(x \right)}, g(x) = x^{2} \log{\left(x \right)}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Provide an integer within [[ ]].

**Answer**: [[your answer here]]

f: x \cos{\left(x \right)}

g: x^{2} \log{\left(x \right)}

correct_answer: 1

answer_format: integer


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \sin{\left(x \right)}, g(x) = e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: \sin{\left(x \right)}

correct_answer: e^{x} \cos{\left(e^{x} \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \log{\left(x \right)}, g(x) = x^{2} \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: \log{\left(x \right)}

correct_answer: \frac{\frac{x}{\tan{\left(x \right)}} + 2}{x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x, g(x) = e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: e^{x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = x^{3}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: x \log{\left(x \right)}

correct_answer: 3 x^{2} \left(\log{\left(x^{3} \right)} + 1\right)


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \cos{\left(x \right)}, g(x) = x^{2} \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: \cos{\left(x \right)}

correct_answer: - x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \sin{\left(x^{2} \sin{\left(x \right)} \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = x^{4}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: 4 x^{3} \left(\log{\left(x^{4} \right)} + 1\right)


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

g: \cos{\left(x \right)}

correct_answer: - \left(\log{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \sin{\left(x \right)}, g(x) = e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: e^{x} \cos{\left(e^{x} \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} \log{\left(x \right)}, g(x) = e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: x^{2} \log{\left(x \right)}

correct_answer: \left(2 \log{\left(e^{x} \right)} + 1\right) e^{2 x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \sin{\left(x \right)}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} \log{\left(x \right)}, g(x) = x. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

g: x

correct_answer: x \left(2 \log{\left(x \right)} + 1\right)


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{5}, g(x) = x^{2} \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: x^{9} \cdot \left(10 \log{\left(x \right)} + 5\right) \log{\left(x \right)}^{4}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = e^{x}, g(x) = x^{2} \cos{\left(x \right)}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

g: x^{2} \cos{\left(x \right)}

correct_answer: 0.41

answer_format: float


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{3}, g(x) = x \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

g: x \cos{\left(x \right)}

correct_answer: 3 x^{2} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \cos^{2}{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = e^{x}, g(x) = x e^{x}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

g: x e^{x}

correct_answer: 82.39


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \log{\left(x \right)}, g(x) = x \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - \tan{\left(x \right)} + \frac{1}{x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \sin{\left(x \right)}, g(x) = \sin{\left(x \right)}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

correct_answer: 0.71


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{5}, g(x) = e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: 5 e^{5 x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - \left(\log{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \cos{\left(x \right)}, g(x) = x e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - \left(x + 1\right) e^{x} \sin{\left(x e^{x} \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{4}, g(x) = \sqrt{x}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Provide an integer within [[ ]].

**Answer**: [[your answer here]]

g: \sqrt{x}

correct_answer: 2


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = e^{x}, g(x) = \sqrt{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{e^{\sqrt{x}}}{2 \sqrt{x}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = e^{x}, g(x) = \sqrt{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{e^{\sqrt{x}}}{2 \sqrt{x}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{\log{\left(\log{\left(x \right)} \right)} + 1}{x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{4}, g(x) = x^{3}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: 12 x^{11}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \cos{\left(x \right)}, g(x) = \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{- \log{\left(x \right)} \sin{\left(\log{\left(x \right)} \right)} + \cos{\left(\log{\left(x \right)} \right)}}{x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = e^{x}, g(x) = x^{2} \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: x \left(2 \log{\left(x \right)} + 1\right) e^{x^{2} \log{\left(x \right)}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{3}{2}}, g(x) = x^{2} e^{x}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{3 \left(x^{2} e^{x}\right)^{\frac{3}{2}} \left(x + 2\right)}{2 x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{3}, g(x) = \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} e^{x}, g(x) = \sin{\left(x \right)}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

correct_answer: 3.00


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x, g(x) = x^{\frac{3}{2}}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{3 \sqrt{x}}{2}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = x^{2} \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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)


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = e^{x}, g(x) = x^{\frac{5}{2}}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{5 x^{\frac{3}{2}} e^{x^{\frac{5}{2}}}}{2}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{4}, g(x) = x^{4}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: 16 x^{15}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} e^{x}, g(x) = \sqrt{x}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

correct_answer: 4.08


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \cos{\left(x \right)}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \sqrt{x}, g(x) = x \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

f: \sqrt{x}

correct_answer: \frac{\sqrt{x \log{\left(x \right)}} \left(\log{\left(x \right)} + 1\right)}{2 x \log{\left(x \right)}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{3}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: 3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \sin{\left(x \right)}, g(x) = x^{3}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

correct_answer: 1.62


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \log{\left(x \right)}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{1}{\tan{\left(x \right)}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} \cos{\left(x \right)}, g(x) = x^{2} e^{x}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

f: x^{2} \cos{\left(x \right)}

correct_answer: -65.17


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \log{\left(x \right)}, g(x) = x^{\frac{5}{2}}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{5}{2 x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{3}, g(x) = x \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: 3 x^{2} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \cos^{2}{\left(x \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x \log{\left(x \right)}, g(x) = x \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \log{\left(x \right)}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{1}{\tan{\left(x \right)}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{5}{2}}, g(x) = x \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{5 \left(x \cos{\left(x \right)}\right)^{\frac{5}{2}} \left(- x \tan{\left(x \right)} + 1\right)}{2 x}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{5}{2}}, g(x) = \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - \frac{5 \sin{\left(x \right)} \cos^{\frac{3}{2}}{\left(x \right)}}{2}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} \log{\left(x \right)}, g(x) = e^{x}. Find f△g at x = 1.

**Rules**:
- Compute the derivative of f(g(x)).
Substitute x = 1.
- Round to two decimal places within [[ ]].

**Answer**: [[your answer here]]

correct_answer: 22.17


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \cos{\left(x \right)}, g(x) = x^{2} \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \sin{\left(x^{2} \sin{\left(x \right)} \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = \cos{\left(x \right)}, g(x) = \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{3}{2}}, g(x) = \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: - \frac{3 \sin{\left(x \right)} \sqrt{\cos{\left(x \right)}}}{2}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{5}{2}}, g(x) = x^{2} \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{\frac{3}{2}}, g(x) = \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{3 \sqrt{\sin{\left(x \right)}} \cos{\left(x \right)}}{2}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} \cos{\left(x \right)}, g(x) = \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{2} \log{\left(x \right)}, g(x) = x^{2} \sin{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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)}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x e^{x}, g(x) = x^{2} \cos{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

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)}}


prompt:
Solve the calculus puzzle:

**Problem**: f(x) = x^{3}, g(x) = \log{\left(x \right)}. Compute f△g.

**Rules**:
- Compute the derivative of f(g(x)).

- Provide your answer in LaTeX enclosed in [[ ]].

**Answer**: [[your answer here]]

correct_answer: \frac{3 \log{\left(x \right)}^{2}}{x}