Question

If `g(0) = 0`, `f'(0) = 2`, `f(0) = 4` and `g'(0) = 3`, then what is the value of `(f @ g)'(0)`?

Answer 1

`6`.

Explanation:

`(f @ g)(x)` can be written as `f(g(x))`.

The chain rule for derivatives deals with composite functions.

It states that for `f(g(x))`, `dy/dx = f'(g(x))g'(x)`

We now insert our given values inside the derivative formula

`f'(g(0))g'(0) = f'(0)(3) = 2(3) = 6`

Hopefully this helps!