Question

In Problems 33–42, use a graphing utility to find the derivative of each function at the given number.
$f\left(x\right)=x^2\sin x$at$\frac{\mathrm{\pi }}{3}$

Short answer

Derivative of $f\left(x\right)=x^2\sin x$at $\frac{\mathrm{\pi }}{3}$is$f\text{'}\left(\frac{\mathrm{\pi }}{3}\right)\approx 2.3621$.

Step-by-step solution

Step 1. Given information

Given function is

$f\left(x\right)=x^2\sin x$

and$x=\frac{\mathrm{\pi }}{3}$

Step 2. Derivative

Enter the function $f\left(x\right)=x^2\sin x$and $x=\frac{\mathrm{\pi }}{3}$in the derivative function of the graphing calculator

The graphing calculator shows that the derivative of the function is$f\text{'}\left(\frac{\mathrm{\pi }}{3}\right)\approx 2.3621$