Calculus Question

Question

If  and , what is ?

Answer 1

The chain rule says for h(x) = f(g(x)), then h’(x) = f ’(g(x)) • g’(x)

In this case f '(x) = cos(x) and g'(x) = 2x

So (f(g(x))' = f '(g(x))•g'(x) = cos(x² - 9)•2x

Plugging in x = 3 we get (f(g(3))' = cos(3² - 9)•2(3) = cos(0)•6 = 1•6 = 6