# How do you differentiate f(x)=sin(4x^2)  using the chain rule?

$8 x \cos \left(4 {x}^{2}\right)$
$f ' \left(x\right) = \cos \left(4 {x}^{2}\right) . \frac{d}{\mathrm{dx}} \left(4 {x}^{2}\right) = \cos \left(4 {x}^{2}\right) \left(8 x\right)$
$\Rightarrow f ' \left(x\right) = 8 x \cos \left(4 {x}^{2}\right)$