Should this be in 2 or 3 dimensions?

Question

anonymous · Answer

$$f(x,y,z)=x^6+y^3+y^4$$And the lack of z term is not a typo.
I'm confused. Should the gradient of this function be $$grad(f)=(6x^5,3y^2+4y^3)$$ or$$grad(f)=(6x^5,3y^2+4y^3,0)$$

anonymous · Answer

i dont know this topic well, but i would assume it would be the second answer because based on the notation f(x,y,z) they want all 3 parts, and they likely know that z=0

anonymous · Answer

Yes, that's what I was thinking, too. The lack of any z terms in the function had me confused.

anonymous · Answer

like i said, i dont know this subject, but in math, it really doesnt matter much if theres a 0 for most applications
example
complex numbers 
4+0i is the same as 4