# What is the derivative of y = cos(a^3 + x^3)?

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

#### Explanation:

Given function

$y = \setminus \cos \left({a}^{3} + {x}^{3}\right)$

differentiating above function w.r.t. $x$ using chain rule

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(\setminus \cos \left({a}^{3} + {x}^{3}\right)\right)$

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

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

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