On Mon, 16 Nov 2009 14:14:27 +0100, Invisible <voi### [at] devnull> wrote:
>
> 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...?

The first one is obviously wrong, unless you mixed up all the f's, g's and  
little circles. It is difficult to tell without context.


>> 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)?

Yes.



> And in general, the Nth composition will be ever more complex as N  
> increases?

Yes.



> ...what I *should* have done of course is
>  http://www.wolframalpha.com/input/?i=derivative+f(f(x))

Except that it is the wrong answer, or rather the wrong question. Wolfram  
thought you meant (f <dot> f)(x), when what you actually meant was (f  
<circle> f)(x).

Just one more reason why it is better to learn the formulas yourself  
instead of relying on a computer to help you all the time.



-- 
FE

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