An Investigation of Implicit Differentiation
This is exactly what the title states, namely, an investigation of implicit differentiation. Often the textbooks deliberately omit proofs or discussion of this matter, and at the most give some paltry abeyance to the chain rule, relations, etc. In looking into the matter further, it seems that multi-variable calculus is required to prove the algorithm of implicit differentiation formally, as well as the implicit function theorem, and so I developed this intuitive approach to help explain the process. I chose to call it an investigation, because unlike my earlier posts about the chain rule below, in which I am speaking with certainty, I have no idea whether this investigation is accurate or proper. I have a hunch, however, that even though some of it is wrong, that much of its core tenants are correct. I think I will email Herbert Gross from M.I.T. at some point and see what he thinks … a student of mine said he actually responds to people's posts on YouTube so when I have some spare time, I will do that! For now, input would be appreciated.
— oemb1905 2017/05/16 02:31
