central_diff2(y,del​tat,d,a)

Finite difference approximation of any order derivative, any accuracy

central_diff2(y,deltat,d,a) returns the dth numeric derivative of y to specified accuracy order deltat^a for evenly sampled data (deltat is constant).
Example:
The third derivative of a time series f sampled at 0.01 second increments to accuracy order deltat^4:
third_derivative_of_f=central_diff2(f,0.01,3,4);
Interior points are calculated using the central difference method. First and last points are calculated using forward and backward difference methods. Intermediate point coefficients are calculated using a Vandermode system. The specified accuracy is maintained for all points.

Source for intermediate point algorithm: http://www.siam.org/books/ot98/sample/OT98Chapter1.pdf