# How do you find the derivative of y= 6cos(x^2) ?

Sep 7, 2014

By Chain Rule, $y ' = - 12 \sin \left({x}^{2}\right)$.

Recall: Chain Rule
$\left[f \left(g \left(x\right)\right)\right] ' = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

In the posted function,
$f \left(x\right) = 6 \cos x$ and $g \left(x\right) = {x}^{2}$
By taking the derivative,
$f ' \left(x\right) = - 6 \sin x$ and $g ' \left(x\right) = 2 x$

Now, we have
$y ' = - 6 \sin \left({x}^{2}\right) \cdot 2 x = - 12 \sin \left({x}^{2}\right)$