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# Find $y^{\prime}$ and $y^{\prime \prime}$$y=\sqrt{x} \ln x$

## $y^{\prime \prime}=-\frac{\ln x}{4 x \sqrt{x}}$

Derivatives

Differentiation

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CA

Catherine A.

October 27, 2020

I've been struggling with Calculus: Early Transcendentals, this is so helpful

SA

Sharieleen A.

October 27, 2020

This will help a lot with my midterm

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

this problem, we want to calculate the 1st and 2nd derivative. So we're going to start off with Y equals mhm route at times natural log effects. And we're going to have to use the product rule here. So I end up getting that white crime is equal to squared of X times the derivative of the natural log events, which is just one of brecht's will have this and then we'll have plus the natural log of X times We know the square root of x derivative is going to be 1/2 UB Act to the -1 House. So I have something like that. Or we can also put the route ex underneath. Then we can also find the um the second derivative in this case which would require us to use either the quotient rule or if we didn't want to use quotient rule, we could use products you again by making this equal to X to the negative one and then keeping this is X to the negative one half.

California Baptist University

#### Topics

Derivatives

Differentiation

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp