# How to find derivative of a 2D curve that goes through ensemble of points?

If we are given a 2D function/curve, then we can get the derivate of that function/curve using central difference or forward difference or backward difference formula at a certain point.

However, if we are given an ensemble of points like for the 2D curve (A) like (-2.5,-3.1),(-2.67,-3.15),(-2.79,-3.21) and so on where each point is (Xi,Yi). Then how can we find the derivatives with respect to X and Y that is dA/dX and dA/dY ?

For 1D curve/function, we could find the derivatives by finding the differences.

• Why not just find the differences the same way, taking v = (x,y) instead of the scalar x in 1D? Then the components of the difference Dv are dA/dx and dA/dy. – AlexanderJ93 Mar 28 '18 at 18:24
• find differences using Euclidean distance? @AlexanderJ93 – user3503711 Mar 28 '18 at 18:26
• Componentwise, i.e. $\Delta_b v_i = \Delta_b (x_i,y_i) = (x_i,y_i)-(x_{i-1},y_{i-1}) = (x_i-x_{i-1},y_i-y_{i-1}) = (\Delta_b x_i, \Delta_b y_i)$ for the backward difference. – AlexanderJ93 Mar 28 '18 at 18:32