The tangent plane of a function ${\displaystyle z = f(x, y)}$ at point ${\displaystyle (x_0, y_0)}$ is equal to

${\displaystyle z-z_0=\frac{\part f}{\part x}(x-x_0)+\frac{\part f}{\part y}(y-y_0)}$

${\displaystyle z=\frac{\part f}{\part x}(x-x_0)+\frac{\part f}{\part y}(y-y_0)+z_0}$