Approximation

If $f(x,y)$ is differentiable at $(x_0,y_0)$ then

$$f(x,y) \approx f(x_0,y_0) + f_x(x_0,y_0)\Delta x + f_y(x_0, y_0)\Delta y$$

Or the same can be written as:

$$\Delta f = \Delta x f_x + \Delta y f_y$$

Linear approximations can be used to estimate values of functions.