   Chapter 11.6, Problem 69E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

If y is a function of x and d y / d x ≠ 0 atsome point, regard x as an implicit function of y and use implicit differentiation to obtain the equation d x d y = 1 d y / d x .

To determine

To prove: The equation dxdy=1dy/dx obtained by using implicit differentiation and concern x as an implicit function of y, if y is a function of x and at some point dy/dx0.

Explanation

Given Information:

The variable y is a function of x and at some point dy/dx0 regards x as an implicit function of y.

Proof:

Consider that y is a function of x,

y=f(x)

Differentiate both sides with respect to y by using chain rule, f(x)=ddx(un)=nun1dudx, where u is the function of x.

1=f(x)dxdyd

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