SOLUTION: Suppose F(x) = f(g(x)) where f(-2)=8 f'(-2)=4 f'(5)=3 g(5)=-2 g'(5)=6 Find F'(5)

Question 1203886: Suppose F(x) = f(g(x)) where
f(-2)=8
f'(-2)=4
f'(5)=3
g(5)=-2
g'(5)=6
Find F'(5)
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Answer: 24

Work Shown

F(x) = f(g(x))
F ' (x) = f ' (g(x)) * g ' (x) ...... chain rule
F ' (5) = f ' (g(5)) * g ' (5)
F ' (5) = f ' (-2) * 6
F ' (5) = 4 * 6
F ' (5) = 24

The relevant given info was
f'(-2)=4
g(5)=-2
g'(5)=6

While the following info wasn't needed
f(-2)=8
f'(5)=3
This likely was designed by your teacher to throw off the student (as a trick answer of sorts)

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