Show that the function `f(x)={x^2sin(1/x),ifx!=0 0,ifx=0` is differentiable at `x=0` and `f^(prime)(0)=0`

Explanation

To show that the function

\[
f(x) =
\begin{cases}
x^2 \sin\left(\frac{1}{x}\right) & \text{if } x \neq 0 \\
0 & \text{if } x = 0
\end{cases}
...