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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.$$y=\ln 8 x^{5}$$

$$5 / x$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

Lectures

01:18

Use the properties of loga…

01:19

02:27

02:09

01:06

03:52

01:50

01:11

02:22

01:49

01:33

Differentiate.$$y=\ln …

01:46

01:17

Find the derivative of eac…

01:22

01:09

Use the General Power Rule…

were asked to find the derivative of natural log of eight X to the fifth power. And what they want you to do is simplify this using the law of logs the first thing that identifies that multiplication so you can split that up using edition. And then, while I'm at it, this power can be written in front. So we're looking at Why equals Natural Auger eight plus five Natural Log of X. Well, now the drift of is very easy to find, because what happens is the derivative. Well, let's look at natural log debate. I don't know what natural log of eight is, but it's always the same number in the drift of a constant, which is what that is, is equal to zero. And then, as we look at five times well, five is a constant. It's just times the derivative of you know, this piece. While the directive of Natural log of X is one over X, and then I think it's pretty clear from there that zero plus anything is that thing. And five times one over X reduces to five over X. So that is your answer. That's a derivative

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