   Chapter 11.3, Problem 13E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If  x y 2 − y 3 = 1 , find  y ' .

To determine

To calculate: The value of y if xy2y3=1.

Explanation

Given Information:

The provided equation is, xy2y3=1.

Formula used:

When y is an implied function of x, obtain dydx by differentiating both sides of the equation with respect to x and then algebraically solve for dydx.

According to the product rule of derivatives,

ddx(uv)=udvdx+vdudx

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x,

dydx=dydududx

Calculation:

Consider the provided equation,

xy2y3=1

First, take the derivative of both sides of the equation with respect to x as,

ddx(xy2y3)=ddx(1)

Now use the product rule of derivatives,

ddx(uv)=udvdx+vdudx

To obtain the derivative of xy2 and use the chain rule,

dydx=dydudu

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