Question

In Problems 33–42, use a graphing utility to find the derivative of each function at the given number.
$f\left(x\right)=x\sin x$at$\frac{\mathrm{\pi }}{4}$

Short answer

Derivative of$f\left(x\right)=x\sin x$at $\frac{\mathrm{\pi }}{4}$is$f\text{'}\left(\frac{\mathrm{\pi }}{4}\right)\approx 1.2625$.

Step-by-step solution

Step 1. Given information

Given function is

$f\left(x\right)=x\sin x$

and$x=\frac{\mathrm{\pi }}{4}$

Step 2. Derivative

Enter the function $f\left(x\right)=x\sin x$and $x=\frac{\mathrm{\pi }}{4}$in the derivative function of the graphing calculator

The graphing calculator shows that the derivative of the function is$f\text{'}\left(\frac{\mathrm{\pi }}{4}\right)\approx 1.2625$