# If f(x) =cos3x  and g(x) = (x+3)^2 , what is f'(g(x)) ?

Feb 23, 2016

First, find the composite function $f \left(g \left(x\right)\right)$, Then, take the derivative with respect to x ...

#### Explanation:

$f \left(g \left(x\right)\right) = \cos \left[3 {\left(x + 3\right)}^{2}\right]$

Now, using the chain rule ...

$f ' \left(g \left(x\right)\right) = - \sin \left[3 {\left(x + 3\right)}^{2}\right] \times 6 \left(x + 3\right)$

hope that helped