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Solve the given problems.Find the general form of the function whose second derivative is $\sqrt{x}$.

$\frac{4}{15} x^{5 / 2}+C_{1} x+C_{2}$

Calculus 1 / AB

Chapter 25

Integration

Section 2

The Indefinite Integral

Integrals

Missouri State University

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:37

Find the derivative of eac…

00:40

02:01

Find the general form of a…

01:14

Calculate the derivative o…

01:06

01:52

Derivatives Find and simpl…

05:01

01:47

00:38

Find a function with the g…

in this problem, we are asked to find the derivative of the function. Why equals negative to over Cube? Root off. It's. We can write this as negative to over X rays to the one third. It simplifies to negative two X rays to the negative one thirds. Now we're going to use the power rule to find the derivative off dysfunction. The power rule states that ddx off X rays to the end is going to be end times X rays to than Manus one where n is any number. So now D y over the ex is equals to d over t X off negative to X rays to the negative one third. Now this negative too is a constant, so we can pull that out of the derivative. So that equals negative two times D d x off x rays to the negative one third. Now using the power rule, the derivative becomes negative one third times X rays to the negative one third minus one now negative times negative is a positive two times one third become scooter ds X rays to the negative one third minus one. So that's negative. Four over three. So that's the derivative off the function

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