I am looking for some symbolic algebra program that allows me to calculate (for example) the $k-$th derivative a function of type $ f (t) = (1 + a (t))^{- 1} $ with $ a $ infinitely differentiable . It is so as not to have to calculate by hand $f ', f '', f'''$ etc.
For example, that the program literally gives me the following: $$f '(t) = - (1 + a (t))^{- 2} a'(t)$$ and so on.
Is there a program like that? Thank you
I'm pretty sure you can do this in Mathematica. When the "D" operator hits something about which it knows nothing, it just says something like $$ D[a, t] $$ to mean "derivative of $a$ with respect to $t$".