# What is the derivative of cos(x^2)?

Sep 4, 2016

$- 2 x \sin \left({x}^{2}\right)$

#### Explanation:

We have: $\cos \left({x}^{2}\right)$

This expression can be differentiated using the "chain rule".

Let $u = {x}^{2} \implies \frac{d}{\mathrm{dx}} \left(u\right) = 2 x$ and $v = \cos \left(u\right) \implies \frac{d}{\mathrm{du}} \left(\cos \left(u\right)\right) = - \sin \left(u\right)$:

=> (d) / (dx) (cos(x^(2)) = 2x cdot - sin(u)

=> (d) / (dx) (cos(x^(2)) = - 2x sin(u)

We can now replace $u$ with ${x}^{2}$:

=> (d) / (dx) (cos(x^(2)) = - 2x sin(x^(2))