If f(x)= sin3x  and g(x) = 2x^2 , how do you differentiate f(g(x))  using the chain rule?

Apr 11, 2016

$\left[f \left(g \left(x\right)\right)\right] ' = 12 x \cos \left(6 {x}^{2}\right)$

Explanation:

$f \left(g \left(x\right)\right) = \sin \left(3 \left(2 {x}^{2}\right)\right) = \sin \left(6 {x}^{2}\right)$

$\left[f \left(g \left(x\right)\right)\right] ' = f ' \left(g \left(x\right)\right) g ' \left(x\right)$

$= \cos \left(6 {x}^{2}\right) \cdot 12 x$

$= 12 x \cos \left(6 {x}^{2}\right)$