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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.$$y=\ln 5 x^{6}$$

$$6 / x$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

McMaster University

Harvey Mudd College

Lectures

01:19

Use the properties of loga…

02:27

01:13

01:50

01:49

02:09

01:06

02:22

01:18

03:52

01:32

Use logarithmic differenti…

01:11

01:46

02:05

Find the derivative.$$…

01:22

02:15

02:20

First use appropriate prop…

So we're asked to find the derivative of natural log of five X to the six if and the advice is good on the problem where they want you to rewrite it. Uh, using your law of logs with the multiplication is split up. As with addition, okay? And I would actually split up one more time because you haven't exponents that could move in front. So we're looking at natural log of five plus six natural log, Becks. And now I think you're ready to take the derivative. Um, So the whole premise is then, well, natural log of five. That's just a constant. Well, we know the derivative of any constant is zero. I don't know what natural log of fives number is, but it's always the same number and derivative of that number is going to be a constant on. The same thing goes here is we're looking at six times so that constant times the derivative of natural law. Globex is one of her ex, um, so that I think pretty clearly simplifies the zero. Plus anything is that thing. And six times in one over X is six over x. So that is your answer

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