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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.$$y=\ln 4 x$$

$$1 / x$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

02:22

Use the properties of loga…

02:55

02:09

01:32

Use logarithmic differenti…

01:19

01:18

01:52

Find the derivative of the…

01:13

02:25

find the derivative of the…

01:06

01:00

Find the derivative of eac…

00:46

01:23

Our task is to find the derivative of natural log of four X Uh, right as y equals. And the hint is that you rewrite the problem as because it's multiplication inside of here that we have natural law before, plus the natural log of X. Well, I remember that the natural before is always the same number. I don't know what that number is. You can use a calculator to find out. But then when I ask you for the derivative well, the derivative of a constant always zero. So that goes away. Whereas the derivative of this piece is just one over X and this is your correct answer. Now, if you're sitting there and saying with that kind of seems wrong, Well, if I were to do this using the chain rule, well, the drift of of natural would be won over that piece and then times the derivative of the inside well, the derivative of the inside it's four. You'll see that the force will cancel because 1/4 of four is one and you're left with one over X s. So it is confirmed that this is correct

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