- Forward difference
- Centered difference
Now, using a computer one can easily compute the value of 
up to a certain approximation. This is one such example where a continuous computation can be approximated using discrete formulation. The key here is the value of 
which should be chosen NOT too large (such that curvatures are totally avoided) nor too small (such that IEEE754 might fail to represent using the system hardware). Now, one can easily write off a C/Java program so as to calculate the differentiation of a function at a given value.
up to a certain approximation. This is one such example where a continuous computation can be approximated using discrete formulation. The key here is the value of which should be chosen NOT too large (such that curvatures are totally avoided) nor too small (such that IEEE754 might fail to represent using the system hardware). Now, one can easily write off a C/Java program so as to calculate the differentiation of a function at a given value.Refer "Press et al, Numerical Recipes, The Art of Scientific Computing, Cambridge Univ Press, III Ed, 2007" for more details.
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