Mathematics: 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) =

If F(x) = f(g(x)), where f(−1) = 5, f ′(−1) = 3,

Ответ:

bellabrill

07.02.2022

Mathematics

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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Ответ:

chantelljenkins2

21.09.2021

Mathematics

Option A

Step-by-step explanation:

You need to multiply the numerator of the first fraction by the numerator of the second fraction and multiply the denominator of the first fraction by de denominator of the second fraction:

$\frac{x+6}{x+3}*\frac{x-6}{x-3}$

$=\frac{(x+6)(x-6)}{(x+3)(x-3)}$

By definition we know that:

(a-b)(a+b)=a^2-b^2

Therefore, you get:

$=\frac{x^2-6^2}{x^2-3^2}$

$=\frac{x^2-36}{x^2-9}}$

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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) =

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