   Chapter 14.5, Problem 30E

Chapter
Section
Textbook Problem

Use Equation 6 to find dy/dx.30. ey sin x = x + xy

To determine

To find: The value of dydx using equation 6.

Explanation

Equation 6:dydx=FxFy=FxFy , where F is the function of xandy ”.

Calculation:

The given equation is, eysinx=x+xy .

Let the function be, F(x,y)=eysinxxxy . (1)

Obtain the equation of dydx by using the equation 6,

dydx=FxFy (2)

Take the partial derivative with respect to x in the equation (1),

Fx=x(eysinxxxy)Fx=ey(cosx)1(1)y=eycosx1y

Thus, the partial derivate of x, Fx=eycosx1y

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