Question

find the first partial derivatives of the function
(x-y)/(x+y)

I know that you have to use quotient rule in this problem but how do you use it when there are two variables within the problem?

Answer 1

make it easier. Use product rule
\[f(x,y)=(x-y)(x+y)^{-1}\\
f_x=-{\partial y\over\partial x}(x-y)^{-1}+(x-y)[-(x+y)^{-2}]{\partial y\over \partial x}\]