I was reading the partial differentiation unit today and came across this theorem. I read this before but never focused towards the proof. Now while seeing the proof, I am thinking how would one get the idea to prove the theorem by considering different functions and using mean value theorem four times.
I am referring Thomas calculus eleventh edition. The book gives a proof in the appendix. (I gave the text book name to be more informative)
My question is as said above "How can one get an idea to prove the theorem".
It would also be helpful if somebody point out some link about how the proof was done by the man who actually proved it.
Simply apply the definition of a derivative and follow this link given above in the comment by Janmarqz for the proof