   Chapter 11.3, Problem 3E ### 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

# In Problems 1-6, find dy/dx at the given point without first solving for y. x y 2 = 8  at (2,2)

To determine

To calculate: The value of dydx for the provided equation xy2=8 at (2,2).

Explanation

Given Information:

The provided equation is, xy2=8 and, the provided point is (2,2).

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,

dydx=dydududx

Calculation:

Consider the provided equation,

xy2=8

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

ddx(xy2)=ddx(8)

Now, use the product rule of derivatives, to obtain the derivative as,

y2dd

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