# How do you find the derivative of y = cos(a^3 + x^3) using the chain rule?

Jan 22, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 3 {x}^{2} \sin \left({a}^{3} + {x}^{3}\right)$

#### Explanation:

using 'chain rule'

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \sin \left({a}^{3} + {x}^{3}\right) . \frac{d}{\mathrm{dx}} \left({a}^{3} + {x}^{3}\right)$

$= - \sin \left({a}^{3} + {x}^{3}\right) . \left(3 {x}^{2}\right)$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = - 3 {x}^{2} \sin \left({a}^{3} + {x}^{3}\right)$