How do you show that the tangent plane at the point $\displaystyle P_{0}(x_{0},y_{0})$, $\displaystyle f(x_{0},y_{0})$ on the surface z=f(x,y) defined by a differentiable function f is the plane:

$\displaystyle f_{x}(x_{0},y_{0})(x-x_{0})+f_{y}(x_{0},y_{0})(y-y_{0})-(z-f(x_{0},y_{0})=0$

OR

$\displaystyle z=f(x_{0},y_{0})+f_{x}(x_{0},y_{0})(x-x_{0})+f_{y}(x_{0},y_{0})(y-y_{0})$