My attempt to find a closed form for a derivative of a product of 'n' functions that are all differentiable.
Then, there is the Leibnitz Theorem which was easy.
Finally my attempt to find a closed expression for Nth derivative of a product of 'n' functions (all differentiable N-fold). I failed miserably on my first attempt as I was unable to find or see the hidden combinatorial pattern. Furthermore, I was not considering a full generalization and hence taking (N=n) in place of which I should have taken (N=m).
I succeeded in my second attempt to do so. And, the closed form is somewhat complicated but remarkably beautiful and elegant.Oh man! That was tough.
There are a few books which I would recommend for interested students.
I will be giving an order to read and understand the material without breaking the learning curve. Additional changes will be made from time to time.