   Chapter 14, Problem 23RE

Chapter
Section
Textbook Problem

If z = xy + xey/x show that x ∂ z ∂ x + y ∂ z ∂ y = x y + z .

To determine

To show: The equation xzx+yzy=xy+z if z=xy+xeyx .

Explanation

Given:

The function is z=xy+xeyx .

Calculation:

The function is z=xy+xeyx (1)

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

zx=x(xy+xeyx)=y+x(eyx(yx2))+eyx(1)=yyxeyx+eyx

Thus, the value of zx is yyxeyx+eyx .

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

zy=y(xy+xeyx)=x+x

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