   Chapter 11.3, Problem 52E ### 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

# Find y" for 1 x − 1 y = 1.

To determine

To calculate: The value of y if 1x1y=1.

Explanation

Given Information:

The provided equation is:

1x1y=1

Formula used:

The quotient rule of derivatives:

ddx[u(x)v(x)]=v(x)du(x)dxu(x)dv(x)dx[v(x)]2

The power rule of derivative,

ddxxn=nxn1

Calculation:

Consider the provided equation:

1x1y=1

Rewrite the equation as:

x1y1=1

Differentiate the both sides of the equation with respect to x as:

ddx(x1y1)=ddx(1)x2+y2y=0

Now, apply the power rule of derivative:

x2+y2y=0y2y=x2y=y2x2

Differentiate both sides with respect to x again as:

y=ddx(y2x2)

Use the quotient rule of derivatives:

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