Question

If `f(x) =-e^(-3x-7)` and `g(x) = -2sec^2x`, what is `f'(g(x))`?

Answer 1

`=12e^(-7)e^(6sec^2x)sec^2xtanx`.

Explanation:

`f(g)=-e^(-3g-7)=e^(-7)e^(6sec^2x)`

So, `f'(g)=(df)/(dx)`

`=e^(-7)e(6sec^2x)(6sec^2x)'`

`=e^(-7)e(6sec^2x)12secx(secx)'`

`=12e^(-7)e^(6sec^2x)sec^2xtanx`.