   Chapter 2.6, Problem 37E

Chapter
Section
Textbook Problem

# Find y ″ by implicit differentiation. sin y + cos x = 1

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

v. Product rule

ddxf*g=fddxg+gddxf

Given:

siny+cosx=1

Calculation:

siny+cosx=1

Differentiate with respect to x

ddxsiny+cosx=1

ddxsiny+ddxcosx=ddx1

cosydydx-sinx=0

cosydydx=sinx

dydx=sinxcosy

Use y' for dydx

y'=sinxcosy

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