I am aware that for a function of two variables f(x,y) a linear approximation of a point f(x,y) close to f(x_0,y_0) can be approximated by the tangent plane approximation f(x_0+\Delta x,y_0+\Delta y)\approx f(x_0,y_0)+f_x(x_0,y_0)\Delta x+f_y(x_0,y_0)\Delta y where \Delta x=x-x_0 and \Delta...