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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Calculate y'.

8. xey = y sin x

To determine

To find: The derivative dydx.

Explanation

Given:

The equation xey=ysinx.

Derivative rule:

product rule: ddx(fg)=fddx(g)+gddx(f).

Calculation:

Obtain the derivative dydx.

xey=ysinx

Differentiate implicitly with respect to x on both sides,

ddx(xey)=ddx(ysinx)xddx(ey)+eyddx(x)=yddx(sinx)+sinxddx(y)  (by product rule)x(eydy

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