Mark James of the Basser Dept. of Computer Science, University of Sydney, Australia asked the following:
Does anyone know of a function that calculates the derivative of a function (that can't be differentiated symbolically) at a given point by numerical means?
Three methods of numerical differentiation are illustrated and examples given in Chapter 6. Numerical Differentiation Algorithm 6.1 Differentiation Using Limits Algorithm 6.2 Differentiation Using Extrapolation Algorithm 6.3 Differentiation Based on n+1 Nodes They can be found in:
NUMERICAL METHODS: Mathematica Notebooks
These files are located at the Wolfram Research, Inc. ftp site