   Chapter 11.6, Problem 14E 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

In Exercises 11-30, find the indicated derivative using implicit differentiation. [HINT: See Example 1.] x y 2 − y = x ; d y d x

To determine

To calculate: The value of dydx for the equation xy2y=x using the implicit differentiation.

Explanation

Given information:

The provided equation is xy2y=x.

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f(x)g(x)+f(x)g(x).

The derivative of function f(x)=un using the chain rule is,

f(x)=ddx(un)=nun1dudx

Where, u is the function of x.

Calculation:

Consider the equation,

xy2y=x

Take ddx of both sides of the above equation,

ddx(xy2y)=ddx(x)ddx(xy2)dydx=ddx(x)

Apply the product rule of derivative to the function (xy2),

(ddx(x)y2+xddx(y2))dydx=1(1y2+xddx(y2))d</

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