# Is there any derivative that the Ti-Nspire can't do?

A fellow student was showing off by quickly have his ti-nspire solve the homework problems. Just wondering if there is any derivative that the ti-nspire would mess up on.

Just where is the limit of ability of the CAS system available.

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The problem is that differentiating most functions you'd think of is trivial. It could possibly be tricked with something like $\sum^\infty_{n=0}a^n \cos b^nx$ (it's nowhere differentiable). Honestly though, I have no clue how capable that system is. –  Karolis Juodelė Nov 8 '12 at 14:53
I would try to play around on Wolfram Alpha. Chances are, if Wolfram Alpha can't do the derivative then neither can the calculator. –  EuYu Nov 8 '12 at 15:51
I would conjecture that there are infinitely many derivatives (which exist) which the calculator cannot do. –  Arkamis Nov 8 '12 at 15:56
A related game is to find integrals that computer algebra systems should be able to do, but can't, because they don't understand what they're doing. One such example is $\int dx/(x^{10000}-1)$. –  Ben Crowell Nov 8 '12 at 15:58
@Ben: Would you mind expanding your comment a bit? I have no intuition for why a CAS "should" be able to do that integral, nor do I know what you mean by "they don't understand what they're doing." –  Jason DeVito Nov 8 '12 at 16:50