New Calculus technique for finding the general formula of derivative

Alright, good good good. I found the alternative method of making a generalized formula of any given function of its derivative and its integral. It is not easy and pretty as the Power formula or its Chain rule consequence. But it is far more general than even the Power formula for it involves every function.

Given any function, the Cell theory can derive the generalized derivative function and derive the generalized integral function.

How is it possible? It is done via the Fourier transform which basically says that any continuous function and all functions are continuous in New Math, is a summation of sine and cosine waves.

In other words, the Fourier Synthesis of any function composed of sine and cosine wavelets is a grand scale Cell theory application. Now I have never seen a proof of the Fourier Synthesis, but Cell theory itself is a given proof of Fourier Synthesis.


Let me try to show how it works. Given any function in math, its derivative and integral in the first cell is computed. Then the derivative is converted (transformed) into a sine or cosine, the same goes for the integral. Take the next cell and do the same conversion and if we look at the function overall and it is patterned smooth function we can thence immediately say the function derivative and function integral from Fourier Synthesis is the general formula for the derivative and integral.

Then of course, we may want to transform the sine and cosine back into a power formula.

So this new method takes the old Fourier Transform and makes it Calculus's new technique to find the general formula of all functions.

I would be curious how the Fourier Synthesis theory was proven, for to my eyes and mind, it is a classic example of Cell theory. In the 10^603 Grid or even the 10^3 Grid where we see perfect circles on the computer screen, every hypotenuse line in a cell is directly translated or transformed to a sine or cosine wavelet of that cell and the area covered by the function in that cell is translated into a sine or cosine wavelet.

So, I am glad I stuck with it, for the Cell theory, I was sure of, had to have a new technique of finding the generalized formula of the derivative and integral of any given function. My new technique is far more universal than the Power Formula and the Chain Rule, but mine is far more difficult and complicated. But in the case of many special functions that have no generalized formula for derivative and integral, here is their moment to shine in the Sun of having that generalized formula.

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Drexel's Math Forum has done an excellent search engine for author posts as seen he
http://mathforum.org/kb/profile.jspa?userID=499986

Now, the only decent search for AP posts on Google Newsgroups, is a search for for it brings up posts that are mostly authored by me and it brings up only about 250 posts. Whereas Drexel brings up nearly 8,000 AP posts. Old Google under Advanced Search
for author, could bring up 20,000 of my authored posts but Google is deteriorating in quality of its searches, likely because AP likes an author search and Google does not want to appear as satisfying to anything that AP likes. If AP likes something, Google is quick to change or alter it.

So the only search engine today doing author searches is Drexel. Spacebanter is starting to do author archive lists. But Google is going in the opposite direction of making author archived posts almost impossible to retrieve.

All the other types of Google searches of AP are just top heavy in hate-spam posts due to search-engine-bombing practices by thousands of hatemongers who have nothing constructive to do in their lives but attack other people.

Now one person claims that Google's deteriorating quality in searches of science newsgroups is all due to "indexing". Well, that is a silly excuse in my opinion, because there is no indexing involved when one simply asks for a author search. No indexing involved if one wants only the pure raw complete list of all posts by a single author. And Google is called the best search engine of our times, yet I have to go to Drexel to see 8,000 of my posts of which I had posted 22,000 to 36,000 posts from 1993 to 2013. It is a shame that Drexel can display 8,000 while Google has a difficult time of displaying 250 of my authored posts. Where the premiere search engine of Google is outclassed by Drexel and even by Spacebanter.

Archimedes Plutonium