Question

Compute the derivative of f(x) = x * sin(x) . Use the result to compute f^ prime ( pi 2 )

Answer 1

Step 1

f(x) = xsinx

Step 2

`\begin{gathered} f(x)=x\sin\left(x\right) \\ \\ f^(\prime)(x)=\sin\left(x\right)+x\cos\left(x\right) \end{gathered}`

Step 3

`\begin{gathered} f^(\prime)((\pi)/(2))=\sin\left((\pi)/(2)\right)+(\pi)/(2)\cos\left((\pi)/(2)\right) \\ \\ f^(\prime)((\pi)/(2))=1 \end{gathered}`

Final answer

A. 1