If the problem is,
Differentiate the following with respect to x.
a) xy^2.
Does it mean,
a) y=xy^2
dy/dx = 2yx(dy/dx) + y^2
so dy/dx=y^2/(1-2yx)
b) xy^2=0
2yx(dy/dx) + y^2 = 0
dy/dx=y^2/2yx
or
c) who knows so no assumption should be made
2yx(dy/dx) + Y^2
Thanks.