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

Dec 25, 2015

$y ' = 2 x \cos \left({x}^{2} + 2\right)$

#### Explanation:

To differentiate this, we have to use ${D}_{x} S \in u = \cos x {D}_{x} u$
So $y = \sin \left({x}^{2} + 2\right)$
$y ' = \cos \left({x}^{2} + 2\right) \left(2 x\right)$
$y ' = 2 x \cos \left({x}^{2} + 2\right)$