Question

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

Answer 1

`f'(g(x)) = -e^(3csc^2x^2)`

Explanation:

`f(x) = -e^x`

`:.f'(x) =-d/dx e^x = -e^x` [Standard differential]

`g(x) = 3csc^2x^2`

Hence, `f'(g(x)) = -e^(g(x))`

`:. f'(g(x)) = -e^(3csc^2x^2)`