### Problem asked by Daniel Phulbani

Find $\frac{dy}{dx}$ if $y = ( \sin 4x^2)^2$.

Let $u = \sin 4x^2$ and $w = 4x^2$, then
$y = u^2$ where $u = \sin w$ and $w = 4x^2$.
We use chain rule to get $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dw} \cdot \frac{dw}{dx}$.
So, $\frac{dy}{dx} = 2u \cdot \cos w \cdot 8x$
= $2 \cdot \sin 4x^2 \cdot \cos 4x^2 \cdot 8x$
= $16x \cdot \sin 4x^2 \cdot \cos 4x^2$