Problem asked by Daniel Phulbani

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

Answer:

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 $