If f(x,y,z)=x2ey√z, then:
∂f/∂x=2xey√z;
∂f/∂y=x2ey√z;
∂f/∂z=½x2ey/√z which can be written ½x2ey√z/z.
The gradient is a vector <2xey√z,x2ey√z,½x2ey/√z>. This can be written in terms of unit vectors: (2xey√z)i+(x2ey√z)j+(½x2ey/√z)k.