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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Find y by implicit differentiation.

x 2 + 4 y 2 = 4

To determine

Tofind:

y"

by implicit differentiation.

Explanation

1) Concept:

To find y, first differentiate the given equation with respect to x. Then solve it for y.

Again differentiate the equation of y with respect to x to get y.

2) Formula:

i. Constant Multiple rule

ddx cfx=  cddxfx

ii. Sum or difference rule

ddxfx ±gx=ddx fx± ddxgx

iii. The power rule

ddxxn=n xn-1

iv. Quotient rule

ddxfg=gddxf-fddxgg2

Given:

x2+4y2=4

Calculation:

x2+4y2=4

Differentiate with respect to x

ddxx2+4y2=4

ddxx2+ddx4y2=ddx4

ddxx2+4ddxy2=4ddx1

2x+8ydydx=0      

8ydydx=-2x

dydx=-2x8y

dydx=-x4y

Use y for <

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