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

Use the properties of logarithms to find the derivative. Hint: It might be easier if you use the properties of logarithms first.$$y=\ln x^{9}$$

$$9 / x$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:29

Use the properties of loga…

02:09

01:19

01:46

01:59

01:06

02:15

01:13

02:22

01:22

02:07

01:18

01:11

03:11

01:44

Use logarithmic differenti…

Yeah, yeah, on this problem were asked to find the derivative of natural log of X to the ninth Power. And the first thing to do is that recognize that that's a power. And so what they want you to do is move that power in front. So it's nine natural log of X. So now the problem Is it really easy? Because, um well, since we have a constant times, anything, the answer is just that Constant. Nine times and derivative of natural law. Globex. Well, the derivative of natural log of X is one over X nine times one of her exes, nine over X. Um, Now, let me just show you if you did the chain rule instead what you did, the chain rule, uh, the drift of of natural of anything is one over that function. But then times adrift of that of that function should be 90 x to the eighth, which eight of those excess would cancel out. Um, you know, you might recognize this rule that you subtract the exponents, which would be nine x of the nega first power, which is the same as this. So using the change rule and using the law of logs gets you the same. Answer nine over x

View More Answers From This Book

Find Another Textbook

01:58

Given the functions you found in Example $59,$ suppose you are later given a…

01:09

Determine the energy of an earthquake if its magnitude is $8.5 .$

01:50

Use -0.000121 as the decay constant for Carbon 14.If an ancient wooden a…

02:46

Suppose $f$ and $g$ are inverse functions and have second derivatives. Show …

02:26

Sketch on the same graph $y=f(x)=2^{x}$ and $y=g(x)=\frac{1}{2^{x}}=2^{-x} .…

02:03

Find and classify, using the second partial derivative test, the critical po…

02:33

Determine the equation of the tangent line at the given $x$ -coordinate.…

02:48

02:42

Determine the area of the region between the given curves.$$f(x)=x^{3} \…

03:02

A demand equation is given by $p=\sqrt{9-x}$, where $p$ is the price per ite…