Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Prove, using (4) that $\frac{d}{d x}\left(x^{1 / 3}\right)=\frac{1}{3 x^{2 / 3}}$.

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

00:31

Write out the proof that $…

03:51

Show that $3 x^{4}+1$ is $…

01:53

Show that $x^{3}$ is $O\le…

01:00

Prove that $\frac{d^{2} y}…

01:14

03:11

Show that $\left(x^{3}+2 x…

01:02

If $x^{2}+y^{2}=t-\frac{1}…

01:05

If $x^{2}+y^{2}=t-\frac{1…

01:06

Show that $$\frac{d}{d x}\…

02:37

Prove that $[3 x]=[x]+\lef…

So if you want to use this equation for here, in order for us to derive this derivative, the first thing we need to do is figure out Well, what is f going to B? Because right now we're assuming that f inverse of X is equal to X to the one third. Um And so if we were to just set this equal to y and then move things around, right, Um, just do you like her? Why? The one third is easy to explain, Cube. Each side we get, Why is he going to execute, which ends up just being Jaffa, Becks. So with this in mind, we can go ahead and take the derivative of this now f prime of X, which is going to give us three x squared, just using powerful. So let's actually right on everything that we have right now. So we have first, that f inverse of X is equal to thanks to the one third we have a FedEx is equal to execute, and then f prime of X is equal to three x squared. So first, let's go ahead and find what the composition of these two is going to be so f prime of F in verse. So that's going to be three X rays to the one third squared, which gives us three X to the two thirds. And then we just need to reciprocate this. So then that would be D by D. X or actually, if we reciprocated alright that first. So one over f prime of F inverse is 1/3 x to the two thirds, which by number four is just the derivative of X to the one third power.

View More Answers From This Book

Find Another Textbook

02:32

Determine the derivative.$$f(x)=x^{2} e^{2 x}-2 x e^{2 x}+4 e^{2 x}$$

02:15

If the cost equation in Exercise I is $C(x)=0.5 x^{2}+x+1,$ what price shoul…

00:40

Determine $f^{\prime}(x)$.$$f(x)=\ln a x, a>0$$

03:43

Differentiate implicitly and then determine the equation of the tangent line…

Determine the energy of an earthquake if its magnitude is 6.7.

03:13

(a) Given $f(x)=2 x^{3}+3 x-4,$ show this function is one-to-one(b) Dete…

01:10

Write the given expression as a sum of logarithms.$$\ln x^{5} \sqrt[4]{y…

03:15

Determine the area of the region between the given curves.$$f(x)=2 x^{2}…

03:10

(a) Given $f(x)=3 x^{5}+2 x^{3}+2,$ show this function is one-to-one.(b)…

03:55