# How do you find the derivative of sin(x^2)cos(x^2)?

Nov 1, 2016

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

#### Explanation:

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

Use product rule and chain rule

$f = \sin \left({x}^{2}\right) , g = \cos \left({x}^{2}\right)$

$f ' = \cos \left({x}^{2}\right) \left(2 x\right) , g ' = - \sin \left({x}^{2}\right) \left(2 x\right)$

$y ' = f g ' + g f '$

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