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Use the properties of logarithms to find the derivative. Hint: It might be easier if you use the properties of logarithms first.$$y=\ln 15 x$$

$$1 / x$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Oregon State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

02:09

Use the properties of loga…

01:18

01:19

01:13

01:11

02:27

01:46

01:22

02:22

02:15

01:44

Use logarithmic differenti…

eso were tasked with finding the derivative of natural log of 15 X. Now they want you to practice the love logs. It's only just show you what What they're talking about here is rewriting the problem as natural August 15 because it's multiplication. Here, you can write is plus natural law. Go back so split them up. Now remember, the natural log of 15 is a number. So when I asked for the derivative Well, the derivative of a constant number is zero eso. There's nothing there, whereas the derivative of natural log of X is just one over X. This is your correct answer on that should make sense. If he did the chain rule in this piece, well, the chain rule would say it's the drift of natural of anything is one over that thing. But then you have to take the directive of the inside, which would be times 15 and these pieces of cancel and it equals what we said it would. So we are correct. A derivative is one over x

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