>> ...what I *should* have done of course is
>>
>> http://www.wolframalpha.com/input/?i=derivative+f(f(x))
>>
>> *facepalm*
> 
> no, because that is a derivative with respect to f not x.

Yes, I figured that out already. (It's actually quite nice that 
Mathematica has an unambiguous notation for this - but you have to 
remember to use it!)

> Many of my students are (hopefully: were) unable to perform a long 
> division or even a long multiplication. They weren't though at school 
> because 'everybody has a calculator at hand anyway'.

At my school, we did nothing *but* long division! Pages and pages and 
pages of it, for years on end. From when I was 14 until I left school, 
_all_ we did in our maths lessons was long division. (Not to mention the 
homework, which was... long division.)

> Someday in the near future all the rest of mathematics and calculus will 
> not be though anymore because 'everybody has an internet connection at 
> hand anyway'. That will be a sad day for our culture.

I'm not sure they teach calculus *currently* in schools. Then again, I'm 
not sure because I didn't attend a normal school... I think in this 
country, if you want to learn about mathematics (not just arithmetic), 
you have to take a special course. I think it's outside the normal 
school curriculum.

Then again, how many people will ever need to know how to compute the 
integral of a polynomial? If you can't add, you're going to have a bit 
of a problem doing your weekly shopping, but there's not much need for 
higher math unless you're working in some specialist industry somewhere. 
(Or you're an academic, which nobody is.)

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