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Let f and g be differentiable functions such that f(3)=5,g(3)=7,f
′
(3)=13,g
′
(3)=6,f
′
(7)=2, and g
′
(7)=0. If h(x)=(fog)(x), then h
′
(3)= ?? A. 14 B. 6 C. 12 D. 10

Respuesta :

If h(x)=(fog)(x) then h'(3) = 12.

Given:

Let f and g be differentiable functions such that f(3)=5,g(3)=7,f'(3) = 13, g'(3) = 6,f'(7) = 2 and g'(7) = 0

h(x)=(fog)(x)

h(x) = f(g(x))

h'(x) = f'(g(x)) * g'(x)

h'(3) = f'(g(3) * g'(3)

= f'(7) * 6

= 2*6

= 12

Therefore If h(x)=(fog)(x) then h'(3) = 12.

Learn more about the differentiable functions here:

https://brainly.com/question/28638304

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