The formula for calculating the divergence at a point in a vector field is not clear to me.
$$\mathbf{v} = [V_x, V_y]$$
here $V$ is a vector and $V_x$ and $V_y$ are its $x$ and $y$ components.
Actual Divergence Equation is as follows $$\text{Divergence}(\mathbf{v}(x ,y)) = \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y}$$
but I feel it should be
$$\text{Divergence}(\mathbf{v}(x,y)) = \frac{\partial v_x}{\partial x} + \frac{\partial v_x}{\partial y} + \frac{\partial v_y}{\partial x} + \frac{\partial v_y}{\partial y}$$
means calculating partial derivative of $x$ with whole vector(instead of $x$ component of the vector) and partial derivative of $y$ with whole vector(instead of $y$ component of the vector).
I am looking for a better explanation.
Thanks