Analytic vs. Analytical I am trying write an article.
Little Summary:
I have developed some tools to analyze derivative of some function $f$. This characterization leads  to better results than previous works that only studied the function itself. 
I am trying to say that:
"Our analytic view of the problem provides a better characterization of blah blah blah "
When I say  analytic view I mean that we not only look at a function but also its derivatives.
My question:
"Our analytic view of the problem provides a better characterization of blah blah blah "
or 
"Our analytical view of the problem provides a better characterization of blah blah blah "

If you have doubts, most probably some other people will also have!
It is always better to be clear, although it is sometimes a difficult decision where to stop (it depends on whether it is for a paper or for a book, whether it is for an abstract or introduction, etc, etc).
Summing up, much better something like: "By looking not only at the function itself but also at its derivatives, in contrast to what Mr.X did in [Y], we are able to provide a better characterization of".
