   Chapter 11, Problem 20RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 15-20, find the indicated derivative.Find the second derivative y " if  x 2 + y 2 = 1.

To determine

To calculate: The second derivative y if x2+y2=1.

Explanation

Given Information:

The provided equation is:

x2+y2=1

Formula used:

When y is an implied function of x, obtain dydx by differentiating both sides of the equation with respect to x and then algebraically solve for dydx.

The quotient rule of derivatives:

ddx(u(x)v(x))=v(x)ddxu(x)u(x)ddxv(x)[v(x)]2

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x and:

dydx=dydududx

The power rule of derivatives:

dxndx=nxn1

Calculation:

Consider the provided equation:

x2+y2=1

First, take the derivative of both sides of the equation with respect to x as:

ddx(x2+y2)=ddx(1)

Now, use the power rule and the chain rule of derivatives:

ddx(x2+y2)=ddx

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