💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

(a) Suppose $ f $ is a one-to-one differentiable function and its inverse function $ f^{-1} $ is also differentiable. Use implicit differentiation to show that$ (f^{-1})'(x) = \frac {1}{f'(f^{-1}(x))} $provided that the denominator is not 0.(b) If $ f(4) = 5 $ and $ f'(4) = \frac {2}{3}, $ find $ (f^{-1})'(5). $

(a) $\left(f^{-1}\right)^{\prime}(x)=\frac{1}{f^{\prime}\left(f^{-1}(x)\right)}$(b) $$ \frac{3}{2} $$

01:33

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Missouri State University

Campbell University

Baylor University

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:53

Suppose $f^{-1}$ is the in…

06:32

Let $f(x)=\cos x+3 x$(…

02:14

01:16

Suppose that the different…

01:58

02:52

In calculus, the differenc…

09:25

Derivativesa. Use limi…

06:56

If $ f $ is a differentiab…

08:35

a. Let $f(x)$ be a functio…

05:03

in this public park every 1st 1 show that at the worst time back to be won over 100 years off. Ex found me know that off. Been worse off eggs. It's a function is one tour is equal X. He detected evidence off both sides with respect to X. You see that F prime off in search of X times. They're a joke in your function. Clams F in worse prime of X. Is it one from this three diesel issue that f commerce prime of eggs is equal to than one over f crime off a humorous off X. And that is same as what is given in the problem statement. All right, that was part of it in part B. Where has to find the worst time? Five. So we're gonna use the question that we just drive some F universe Primer five is equal to one over. Prime asked in Worse off fire. What? Has that been worse? A fire. Well, you know that effort for is it for if 405 it means that you're worse off 54 So then we have on over prior or four and primal forces, Given that history, he said. It is over to over three, so we find the answer to be then three or two.

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Suppose $f^{-1}$ is the inverse function of a differentiablefunction $f$…

Let $f(x)=\cos x+3 x$(a) Show that $f$ has a differentiable inverse.…

Suppose that the differentiable function $y=f(x)$ has an inverse and that th…

In calculus, the difference quotient $\frac{f(x+h)-f(x)}{h}$ of a function $…

Derivativesa. Use limits to find the derivative function $f^{\prime}$ fo…

If $ f $ is a differentiable function, find an expression for the derivative…

a. Let $f(x)$ be a function satisfying $|f(x)| \leq x^{2}$ for $-1 \leq x \l…