# How do you differentiate sin(x^4)?

Aug 4, 2017

$4 {x}^{3} \cos \left({x}^{4}\right)$

#### Explanation:

By the chain rule
$\left(\sin \left({x}^{4}\right)\right) ' = \left({x}^{4}\right) ' \sin ' \left({x}^{4}\right)$

$= 4 {x}^{3} \sin ' \left({x}^{4}\right)$ by the power rule

And since $\sin ' \left(x\right) = \cos \left(x\right)$

$\left(\sin \left({x}^{4}\right)\right) ' = 4 {x}^{3} \cos \left({x}^{4}\right)$