If I have a scalar potential $\phi = \frac{\cos(\theta)}{r}$ and $\vec{V}=\nabla\phi$ and I am going to find the vector field $\vec{V} = \left(\frac{\partial \phi}{\partial r}, \frac{1}{r}\frac{\partial \phi}{\partial \theta}\right)$. I get $\left(-\frac{\cos(\theta)}{r^2},-\frac{\sin(\theta)}{r^2}\right)$. If I change this expression into cartesian coordinates I get $\vec{V} = \left(\frac{-x}{(x^2+y^2)^{3/2}}, \frac{-y}{x^2+y^2)^{3/2}}\right)$
However, if I change $\phi$ to Cartesian coordinates first and use $\vec{V} = \left(\frac{\partial \phi}{\partial x}, \frac{\partial \phi}{\partial y}\right)$, I get $\vec{V} = \left(\frac{y^2 -x^2}{(x^2 + y^2)^2}, \frac{-2xy}{x^2+y^2)^{2}}\right)$
This looks like inconsistency to me...what is going on?