>> Oh, I did Google it. I just didn't comprehend the answer. (In 
>> particular, I've already read the Wikipedia entry.)
> 
> What is so difficult to understand about it?

One formula appears to say the derivative is f(x) * g(x), and another 
appears to say it's f'(g(x)) * g'(x), which is different, but these are 
supposed to be different notations for the same formula...?

> I thought function 
> composition would be one of the areas of math that you were actually 
> good at, given your fanatical obsession with a certain functional 
> programming language.

Function composition I get. It's what that does to the derivating I 
can't quite wrap my brain around.

> Anyway:
> 
> The derivative of f( g(x) ) is f'(g(x))*g'(x).
> 
> Substitute the inner function into the derivative of the outer function, 
> and then multiply by the derivative of the inner function.

> df(f(x))/dx = f'(f(x))*f'(x) = g(f(x))*g(x)

Right. So basically, the function I'm looking for is f'(f(x))*f'(x)?

So presumably the derivative of f(f(f(x))) is going to be something like 
f'(f(f(x))) * f'(f(x)) * f'(x)? And in general, the Nth composition will 
be ever more complex as N increases?

Oh dear.

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