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NeX [460]
3 years ago
11

Define the function

Mathematics
1 answer:
miss Akunina [59]3 years ago
7 0

Given that

g(x) = x^3 + x

the inverse g^{-1}(x) is such that

g\left(g^{-1}(x)\right) = g^{-1}(x)^3 + g^{-1}(x) = x

or

g\left(f(x)\right) = f(x)^3 + f(x) = x

Differentiating both sides using the chain rule gives

3f(x)^2f'(x) + f'(x) = 1 \\\\ f'(x) \left(3f(x)^2+1\right) = 1 \\\\ f'(x) = \dfrac1{3f(x)^2+1}

Then the derivative of <em>f</em> at 2 is

f'(2) = \dfrac1{3f(2)^2+1} = \boxed{\dfrac14}

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Answer:

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Step-by-step explanation:

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4 years ago
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3 years ago
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katovenus [111]

Answer:

spin it 35 times

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2 years ago
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4 0
4 years ago
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Answer:

b.× = 14 16

Step-by-step explanation:

<em>#</em><em>s</em><em>t</em><em>a</em><em>y</em><em> </em><em>safe</em>

hope it helps

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