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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.$$y=\ln \sqrt{2 x+1}$$

$$\frac{1}{2 x+1}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

McMaster University

University of Michigan - Ann Arbor

Lectures

02:09

Use the properties of loga…

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02:22

02:15

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Use logarithmic differenti…

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right. Eso This problem is asking for the drift of while using several one mall vlog. But then the problem The problem is pretty easy. It once you do that eso the manipulation is understand that that's the same thing as the square root is the same thing as to the one half power. So then you can take that power and move that in front. So we're really looking at why equals one half natural log of two X plus one. Now we really can't do anything else besides that. Um, but this makes the problem easier because then when I ask you for the derivative well, a constant times, something the derivative us that same constant times, that same thing eso the derivative of natural log is one over that piece times the derivative of the inside of that peace. Will the derivative of to excess too on directive A 10 So that's not actually there anymore. And so what happens is that one half of two later cancel each other out. So this answers simply, you know, simplified. It comes out to 1/2 X plus one and we're done. That's the right answer

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