   Chapter 4.5, Problem 8SWU ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 7 and 8, find dy/dx implicitly. x 2 y − x y 2 = 3 x

To determine

To calculate: The value of dydx for the equation x2yxy2=3x using the implicit differentiation.

Explanation

Given information:

The provided equation is x2yxy2=3x.

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 x2yxy2=3x,

Take ddx of both sides of the above equation,

ddx(x2yxy2)=ddx(3x)

Apply product rule of derivative function to (x2y) and (xy2),

ddx(x2y)ddx(xy2)=3(x2ddx(y)+yddx(x2))(xddx(y2)+y2ddx(x))=3(x

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