Mathematics: Find the value of the given function s derivative at x=3 f(x)=k(g(x)) g(x)=2x-x^2 k (-3)=2 f (3)=[]

Find the value of the given function s derivative

Ответ:

Xavier2712

20.01.2022

Mathematics

Explanation:

According to the chain rule, if we have a function:

f(x)=k(g(x))

The derivative at a point will be:

f'(a)=k'(g(a))g'(a)

We know that:

$f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}$

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Ответ:

marley462847

19.07.2021

Mathematics

x=2

Step-by-step explanation:

4x-6=6-2x

(add 2x and 6 to both sides)

6x=12

(divide by six)

x=2

Double Check:

4(2)-6=2

6-2(2)=2

4(2)-6=6-2(2)

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Find the value of the given function's derivative at x=3

f(x)=k(g(x))
g(x)=2x-x^2
k'(-3)=2
f'(3)=[]

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Find the value of the given function's derivative at x=3 f(x)=k(g(x)) g(x)=2x-x^2 k'(-3)=2 f'(3)=[]

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Answers on questions: Mathematics

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Find the value of the given function's derivative at x=3

f(x)=k(g(x))
g(x)=2x-x^2
k'(-3)=2
f'(3)=[]