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# Find $y'$ and $y".$$y = \frac {\ln x}{l + \ln x}$

## $y^{\prime}=\frac{1}{(x)(1+\ln x)^{2}}$ and $y^{\prime \prime}=-\frac{3+\ln x}{x^{2}(1+\ln x)^{3}}$

Derivatives

Differentiation

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AO

Alex O.

June 12, 2020

it should be a 2 instead of a 3 in the numerator

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

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### Video Transcript

Miss Strom wears to find persons secondary it off natural about Do I travel? Prosecution? Thanks. Let's start for a person that they were gonna expression fool. But there were still punching the numerator. What's 555 denominated minus function The numerator multiplied by a bunch of denominated. What's X? You have my function, you know, Major spread now this gives us on our necks. Was ex officer national level like so ex Marta station Look up X over eggs divided by one plus nation Local ex for years We know why we have the first words as for nor explain for for station of X square All right, we're going to use now course central or more Time to point second derivatives. So we have zero minus Baraquio First function, which is one times the second function border were false actually spread, plus the first function loves Black by Derek A second function which is to fall in presidential of eggs time spiritual or plus naturally Perfect, which is one of ex derided by function and dinner may spread which is expert times One nation over X city for over exes will cast. Love is you can see we have one plus natural affects here and we have a plus. National affects their We can factor that out. He have negative off one plus there she'll ever x my flight by a warm plus nation Logan. Thanks. Plus two he wanted by X squared times one plus national of affects. Before this will cancel out, spar will be free. So from this, then we find the second derivative to be negative off three plus nation Log of X divided by X for a time for presidential. Exe cute.

#### Topics

Derivatives

Differentiation

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp