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.

$F'(x)=\dfrac{d}{dx}f(g(x))$

Using chain rule, we get

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

Now, put x=5.

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

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

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

$F'(5)=24$

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