# Nonlinear solver & Differentiation Chain Rule

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 February 5, 2009, 07:36 Nonlinear solver & Differentiation Chain Rule #1 Frank Guest   Posts: n/a I am trying to solve a horrible function using newtons method and need to differentiate it. There is only one unknown variable x. The problem is that the function I am looking at is a function of a function of a function... very nonlinear and nasty. I don't have access to my elementary textbooks from work and am pretty rusty when it comes to differentiation. Am I right in thinking that I can repeatedly apply the chain rule, e.g du/dx = du/da * da/db * db/dx I'm pretty sure this is right but wanted to make sure before I start sticking coefficients in the software.

 February 5, 2009, 08:42 Re: Nonlinear solver & Differentiation Chain Rule #2 Farid Guest   Posts: n/a Yes of course!You have to use the chain rule until the expression is easy enough to compute db/dx. If it's a really nasty expression, I would suggest you to do it with Matlab! Otherwise you might make a mistake by solving it by hand. syms x; (new line) y = nasty espression; (new line) diff(y,x) That's it Cheers Farid

 February 6, 2009, 03:17 Re: Nonlinear solver & Differentiation Chain Rule #3 Praveen. C Guest   Posts: n/a If you have a computer program that is computing these functions, then you can use automatic differentiation. No pain in this. See http://www.autodiff.org There are AD tools for fortran, C and even matlab.

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