   Chapter 2.6, Problem 24E

Chapter
Section
Textbook Problem

# Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find d x / d y . y sec x = x tan y

To determine

To find:

dxdy

by using implicit differentiation.

Explanation

1) Formula:

i. Product Rule:

ddxf*g=fddxg+gddxf

2) Given:

ysecx=xtany

3) Calculation:

ysecx=xtany

Differentiate with respect to y

ddyysecx=ddyxtany

Use Product rule for differentiation

yddysecx+secxddyy=xddytany+tanyddy(x)

ysecxtanxddyx+secx*1=xsec2y+tanyddy(x)

ysecxtanxddyx+secx=x<

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