z=f(x/y) Using partial derivatives (Multivariable calculus) find dz/dy. I know that dz/dx is f'(x/y)/y. I am given the following choices:
A) 0
B) 1
C) f '(x/y)/x
D) f '(x/y)/y
E) xf '(x/y)/x
F) yf '(x/y)/y
G) xf '(x/y)/x^2
H) yf '(x/y)/y^2
I) xf '(x/y)/y^2
J) yf '(x/y)/x^2
K) -xf '(x/y)/x^2
L) -yf '(x/y)/y^2
M) -xf '(x/y)/y^2
N) -yf '(x/y)/x^2
O) none of the above
I know for sure that D is not it because that is dz/dx. I also assume that anything which has values that cancel out such as xf'(x/y)/x are not it, so that takes out E,F. In that case, G & H are equivalent to C & D, so all those are out of the question. Even though I don't think A and B are right, I'm not 100%, so I'll leave them in.
My options are now A B I J K L M N O. Can someone help me reason through this and figure out which one is right, if any?