Question

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) =

Answer 1

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.