# If f(x)= - e^(5x  and g(x) = 3 x , how do you differentiate f(g(x))  using the chain rule?

Sep 30, 2016

$f ' \left(g \left(x\right)\right) = - 15 {e}^{15 x}$

#### Explanation:

To obtain f(g(x)) substitute g(x) in for x in f(x).

rArrf(g(x))=f(color(red)(3x))=-e^(5(color(red)(3x))=-e^(15x)

differentiate using the $\textcolor{b l u e}{\text{chain rule}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$f ' \left(g \left(x\right)\right) = - {e}^{15 x} . \frac{d}{\mathrm{dx}} \left(15 x\right) = - 15 {e}^{15 x}$