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.

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

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.