Mathematics: You can find the derivative of the inverse function by differentiating the inverse explicitly, or by using the formula:

You can find the derivative of the inverse function

Ответ:

decoreyjpaipxv

13.03.2022

Mathematics

If a function f(x) has an inverse f ⁻¹(x), then by definition

$f\left(f^{-1}(x)\right) = x$

Differentiating both sides with respect to x yields

$f'\left(f^{-1}(x)\right) \times \left(f^{-1}\right)'(x) = 1 \implies \left(f^{-1}\right)'(x) = \dfrac1{f'\left(f^{-1}(x)\right)}$

Now, if f(a) = b and b = f ⁻¹(a), then

$\left(f^{-1}\right)'(a) = \dfrac1{f'\left(f^{-1}(a)\right)} = \dfrac1{f'(b)}$

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Ответ:

hanacat6174

13.08.2022

Mathematics

$9\frac{2}{6}-6\frac{5}{6}\\\\1=\frac{6}{6}\ therefore\ 9\frac{2}{6}=8+1\frac{2}{6}=8+1+\frac{2}{6}=8+\frac{6}{6}+\frac{2}{6}=8\frac{8}{6}\\\\9\frac{2}{6}-6\frac{5}{6}=8\frac{8}{6}-6\frac{5}{6}=(8-6)+(\frac{8}{6}-\frac{5}{6})=2+\frac{8-5}{6}=2\frac{3}{6}=2\frac{3:3}{6:3}\\\center=\boxed{\boxed{2\frac{1}{2}}}$

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You can find the derivative of the inverse function by differentiating the inverse explicitly, or by using the formula:

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