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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find dy/dx by implicit differentiation.

10. xey = x – y

To determine

To find: The derivative dydx by implicit differentiation.

Explanation

Given:

The equation xey=xy.

Derivative rules:

(1) Chain rule: If y=f(u) and u=g(x)  are both differentiable function, then

dydx=dydududx.

(2) Product rule: ddx(fg)=fddx(g)+gddx(f)

Calculation:

Obtain the derivative of xey=xy implicit with respect to x.

xey=xy

Differentiate with respect to x on both sides,

ddx(xey)=ddx(xy)ddx(xey)=ddx(x)ddx(y)ddx(xey)=1dydx

Apply the product rule (2) and the chain rule (1),

xddx(e

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