Partial derivative of a modular function?

[hotlip1]

Given f(x,y)=|x-y^2+3| I'm asked to calculate df/dx and df/dy.

f(x,y)=x-y^2+3 if x-y^2+3>=0
f(x,y)=-x+y^2-3 if x-y^2+3<0

df/dx=1 if x-y^2+3>=0
df/dx=-1 if x-y^2+3<0

df/dy=-2y if x-y^2+3>=0
df/dy=2y if x-y^2+3<0


Is it ok to say this?