Df(x_0,y_0)(h_1, h_2)=\left[ {\begin{array}{cc}
 \frac{\partial f}{\partial x}(x_0,y_0) & \frac{\partial f}{\partial y}(x_0,y_0)
 \end{array} } \right] \cdot \left[ {\begin{array}{cc}
 h_1 \\ h_2
 \end{array} } \right]=\frac{\partial f}{\partial x}(x_0,y_0)h_1 + \frac{\partial f}{\partial y}(x_0,y_0)h_2