Question

If `f(x) =-e^(2x+4)` and `g(x) = tan3x`, what is `f'(g(x))`?

Answer 1

`f'(g(x)) = -2e^(2tan(3x)+4)`

Explanation:

`f'(g(x))` indicates that we need to take the derivative of `f`, and then plug in `g(x)` for `x`.

First, let's find `f'(x)`:

We know that `d/dxe^u = e^u d/dx(u)`

Therefore:

`d/dx(-e^(2x+4)) = -e^(2x+4) * d/dx(2x+4)`

`= -2e^(2x+4)`

So `f'(x) = -2e^(2x+4)`.

We also know that `g(x) = tan(3x)`

Therefore, `f'(g(x)) = -2e^(2tan(3x)+4)`

Final Answer