#
PsiL_{A}B Help Manual
Page

## Section:
Derivations of a function

## Name:
derivate

**Iterates the derivation of a function f. **

This functions performs a numerical derivativ of a function f depending on one variable x. It returns the the derivative at a point x _{0 }by Ridders' method of polynomial extrapolation, as described in Numerical Recipes.

[ y':float ] = derivate

(func:float->float)

(x:float)

(err:float)

unit

The *err *argument sets the maximal error limit excepted for a successfull iteration. This function can only be used for the first derivative of a function. The algortihm fails on data produced by himselfes! There is another derivative module, called *DyDx *. It's based on a multiple point calculation around the *x *_{0 }point. In contrast to this iteration, the *DyDx *module can always be used for higher derivatives, but without error consideration.

[] let y = fun x -> sin x ;;
val y : float -> float = <fun>
[] derivate y 0.5 () ;;
- : float = 0.87758256189
[] cos 0.5 ;;
- : float = 0.87758256189

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