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?

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?

anonymous · Answer

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