Mathematical software that handles symbolically the derivative of parametrically defined functions?

Question

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?