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

1 Answer
Dec 4, 2016

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!