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If F(x) = f(g(x)), where f(−1) = 5, f ′(−1) = 3, f ′(5) = 3, g(5) = −1, and g ′(5) = 8, find F ′(5). F '(5) =

User Vick
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1 Answer

4 votes

Given:


F(x)=f(g(x))

where,
f(-1)=5,f'(-1)=3,f'(5)=3,g(5)=-1,g'(5)=8.

To find:

The value of
F'(5).

Solution:

We have,


F(x)=f(g(x))

Differentiate with respect to x.


F'(x)=(d)/(dx)f(g(x))

Using chain rule, we get


F'(x)=f'(g(x))g'(x)

Now, put x=5.


F'(5)=f'(g(5))g'(5)


F'(5)=f'(-1)* 8
[\because g(5)=-1,g'(5)=8]


F'(5)=3* 8
[\because f'(-1)=3]


F'(5)=24

Therefore, the value of
F'(5) is 24.

User Coo
by
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