Question

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

Answer 1

`f'(g(x))=-15e^(15x)`

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 `color(blue)"chain rule"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(d/dx(e^x)=e^x)color(white)(a/a)|)))`

`f'(g(x))=-e^(15x).d/dx(15x)=-15e^(15x)`