suppose i have a very simple function f(x,y) = x*y.

now i have a ratio that takes the partial derivative in respect to x and divides it by the partial derivative in respect to y. so we have D = ( del f / del x) / (del f / del y) alright. if i do it the normal way, obviously we get D = y / x as our answer.

what i dont get is this: if i try to simplify the fraction of D, then i would get D = del y / del x. now that doesnt make sense. am i not allowed to cancel out partial derivatives or what am i not seeing here?