3 years ago

Help i would like an explanation if possible and Im not smart

Mathematics

1 answer:

sesenic [268]3 years ago

7 0

Answer:

3/16

Step-by-step explation

1/2 x 3/8

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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) =

sattari [20]

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.

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