James Stewart

ISBN: 9781305266643

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.

Equation 6: “ dydx=−∂F∂x∂F∂y=−FxFy , where F is the function of x and y ”.

Calculation:

The given equation is, cos(xy)=1+siny .

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

∂F∂x=∂∂x(cos(xy)−1−siny)=∂∂x(cos(xy))−∂∂x(1)−∂∂x(siny)=−sinxy(y)−0−0Fx=−ysin(xy)

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

Check out a sample textbook solution.

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

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Math
Calculus Multivariable Calculus 8th Edition

Use Equation 6 to find dy/dx.

28. cos(xy) = 1 + sin y