Find a function f such that F = del f.

F(x, y, z) = 2xy i + (x2+10yz) j + 5y2 k

I have:

fx = 2xy
fy = x^2+10yz
fz = 5y^2

Integrate w.r.t x, f = x^2(y) + g(y,z)

Diff w.r.t. y, fy = x^2 + gy(y,z) so gy(y,z) = 10yz

I'm stuck here.