Differentiation

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Contributor
Posts: 31

Differentiation

Hello all;

How can i find the nth derivative of an function?

for example:      dn/dxn (exp(-x)*x^3)      (for n=2)

SAS Super FREQ
Posts: 3,752

Re: Differentiation

Posted in reply to RaniaMamdouh

The NLPFDD function in SAS/IML software computes the finite difference approximation of first and second derivatives for vector-values function (or scalar-valued, as you have here).

SAS/IML(R) 13.1 User's Guide

Here's an example: Optimizing? Two hints for specifying derivatives - The DO Loop

Also, if you have a time series with evenly spaced time points, you can use the DIF function in SAS/IML software or in the DATA step. See

The DIF function: Compute lagged differences and finite differences - The DO Loop

Contributor
Posts: 31

Re: Differentiation

How i can find the 10th derivative ?

SAS Super FREQ
Posts: 3,752

Re: Differentiation

Posted in reply to RaniaMamdouh

Foryour function you can find the 10th derivative analytically by repeated application of the product and chain rule. Tenth derivatives do not often arise in numerical computations.

Contributor
Posts: 31

Re: Differentiation

Is there any example for application of the product and chain rule?

SAS Super FREQ
Posts: 3,752

Re: Differentiation

Posted in reply to RaniaMamdouh

Have you taken calculus? These are just the names of the usual rules for differentiation. For example, see your calculus book or see Product rule - Wikipedia, the free encyclopedia and Chain rule - Wikipedia, the free encyclopedia

Contributor
Posts: 31

Re: Differentiation

I mean how can i apply the product and chain rule in SAS???

SAS Super FREQ
Posts: 3,752

Re: Differentiation

Posted in reply to RaniaMamdouh

SAS does not have a procedure that outputs symbolic derivatives.  You will have to do it by hand or use a symbolic algebra package such as Mathematica, Maple, or Maxima.

Contributor
Posts: 31

Re: Differentiation

Ok

thank you so much

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