Question

(chain rule and partial derivatives)
If z = y + f(x^2 - y^2), where f is differentiable, show that y(del(z)/del(x)) + x(del(z)/del(y)) = x

Answer 1

\[\frac{\partial z}{\partial y}=1+\frac{d f}{d(x^2-y^2)}(-2y) \\ \frac{\partial z}{\partial x}=\frac{d f}{d (x^2-y^2)}(2x)\]

Answer 2

multiply first equation by x
second equation by y
add them up and see what you get

Answer 3

OH MAN okay thanks a bunch, I see where I went astray now

Answer 4

no prob :)