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Solve the given problems by finding the appropriate derivatives.Find any values of $x$ for which the derivative of $y=\frac{x^{2}}{\sqrt{x^{2}+1}}$ is zero. View the curve of the function on a calculator to verify the values found.

$$x=0$$

Calculus 1 / AB

Chapter 23

The Derivative

Section 7

The Derivative of a Power of a Function

Derivatives

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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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