   Chapter 14.5, Problem 28E

Chapter
Section
Textbook Problem

Use Equation 6 to find dy/dx.28. cos(xy) = 1 + sin y

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, cos(xy)=1+siny .

Let the function be, F(x,y)=cos(xy)1siny (1)

Obtain the equation dydx by using the equation 6,

dydx=FxFy (2)

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

Fx=x(cos(xy)1siny)=x(cos(xy))x(1)x(siny)=sinxy(y)00Fx=ysin(xy)

Thus, the partial derivate, Fx=ysin(xy)

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