if y = 2f(g(x)), then d^2y / dx^2 =

Question

A. f''(g(x)) * g'(x)
B. f''(g(x)) * [g'(x)]^2
C. 2f''(g(x)) * [g'(x)]^2
D. 2f''(g(x)) * [g'(x)]^2 + 2f'(g(x)) * g''(x)
E. Cannot be determined

Answer 1

use the chain rule
y' = 2f'(g)*g'(x)

now use the product rule
y" = 2f"(g)g'(x)*g'(x) + 2f'(g)g"(x)

Answer 2

oobleck is correct; answer d is the right answer!