Problem

Find the second derivative of each of the given f…

Problem 26 Easy Difficulty

Find the second derivative of each of the given functions.
$$y=\frac{8 x}{\sqrt{9-x^{2}}}$$

Answer

$\frac{112 x\left(9-x^{2}\right)^{3 / 2}+6 x\left(72+56 x^{2}\right)\left(9-x^{2}\right)^{1 / 2}}{\left(9-x^{2}\right)^{3}}$

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 23

The Derivative

Section 9

Higher Derivatives

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Video Transcript

in order to find the derivative off the given problems, let's start by first identifying the inner and outer functions. The inner function in this case, you is going to be equal to X square plus nine. The ultra function Why is going to be equal to you raised to the power off one by three since we're going to apply the chain will in order to find that their abated. So we need to first evaluate you by the X, which is going to be equal to two X next, using the power rule reevaluate de vie de you, which is going to be equal to one by three U to the power off negative to buy tree The para rule states that divided the X is equal to divide by the U into do you by D x. All we have to do is to replace the values that they've already replaced it. We've already calculated for each of those hits one by three you raised to the power off negative to buy three is going to be replaced with d y by d you, whereas you by D. X is going to be replaced by two ex acid already evaluated. Next, we're going to simplify the equation and put in the value off you does. Our answer becomes to accident three Putting in the value off you X squared plus nine raised to the power off. Negative two by three In order to simplify Furthermore de bye bye DX becomes two x divided by three X square plus nine to the power off to buy three.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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