# If f(x)= sin3x  and g(x) = 2x^2 -3x , how do you differentiate f(g(x))  using the chain rule?

Jul 13, 2018

$f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right) = \cos \left(6 {x}^{2} - 9 x\right) \cdot \left(12 x - 9\right)$

#### Explanation:

We have

$f \left(g \left(x\right)\right) = \sin \left(3 \left(2 {x}^{2} - 3 x\right)\right) = \sin \left(6 {x}^{2} - 9 x\right)$
By the chain rule

$f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$ we get

$\cos \left(6 {x}^{2} - 9 x\right) \cdot \left(12 x - 9\right)$