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From M.S.'s question "A general formula for the n-th derivative of a parametrically defined function", the above question came to me.

I wasn't able to make Sage or Matlab doing something like the derivative of $t^3+t^4$ respect to $t^2$ via symbolic computation, and moreover it seems to me that they are not able to handle an undefined expression like $$\begin{align*}x&=f(t)\\y&=g(t)\end{align*}$$ where they give error since $f$ and $g$ are "undefined".

But, as in M.S. example in his linked question, at least about derivatives, they follow some rigorous mechanics, I mean they are "defined" regarding some properties. So maybe wouldn't be hard to implement a package that do stuffs like deriving general parametrically defined functions; so isn't yet there some mathematical software capable of doing such computations like in M.S.'s case?

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Mathematica doesn't have much trouble: FullSimplify[NestList[(D[#, t]/f'[t]) &, g'[t]/f'[t], 10]] –  J. M. Oct 1 '11 at 12:27
    
@M.S. thanks. I'm often wondering what mathematical software is worth spending more time on. –  Emanuele Natale Oct 1 '11 at 12:40
    
I sure as peas ain't M.S., Emanuele, but: MATLAB is pretty good in the numerics department, while Mathematica and Maple do well with symbolics. –  J. M. Oct 1 '11 at 12:42
    
@J.M. yep, sorry: lapsus linguae speaking about M(athematical)S(oftware) :) –  Emanuele Natale Oct 1 '11 at 12:52

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