   Chapter 14, Problem 39RE

Chapter
Section
Textbook Problem

If z = y + f(x2 – y2), where f is differentiable, show that y ∂ z ∂ x + x ∂ z ∂ y = x

To determine

To show: The function, z=y+f(x2y2) where f is differentiable satisfies the given equation yzx+xzy=x .

Explanation

Proof:

The given function is, z=y+f(x2y2) .

The equation yzx+xzy=x is to be proved.

Obtain the value of yzx+xzy .

yzx+xzy=yx[y+f(x2y2)]+xy[y+f(x2y2)]=y2x(1)+yx(f(x2y2))+x

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