# If f(x) =xe^(5x+4)  and g(x) = sin3x , what is f'(g(x)) ?

Apr 14, 2017

$f ' \left(g \left(x\right)\right) = {e}^{5 \sin \left(3 x\right) + 4} \left(5 \sin \left(3 x\right) + 1\right)$

#### Explanation:

First we find the derivative of $f \left(x\right) = x {e}^{5 x + 4}$

$\frac{d}{\mathrm{dx}} \left(x {e}^{5 x + 4}\right) = {e}^{5 x + 4} \left(5 x + 1\right)$

So $f ' \left(x\right) = {e}^{5 x + 4} \left(5 x + 1\right)$

Now we plug $\sin 3 x$ everywhere we have a $x$ in $f ' \left(x\right)$.
$f ' \left(g \left(x\right)\right) = {e}^{5 \sin \left(3 x\right) + 4} \left(5 \sin \left(3 x\right) + 1\right)$