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>> ...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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