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# diffrentiation by ab-initio method Watch

1. can any help me out how to differentiate x^x by ab-initio method or first principle

2. Expand both expressions binomially, noting that . The first expression will need a little more work afterwards.
3. really thnx a lot for helpn me out
4. (Original post by Lord of the Flies)
The first expression will need a little more work afterwards.
Starting from the beginning, I wrote out the first-principles definition of , stared at it and found it impossible. I thought it was a bit more "obvious what to do at each step" to:
• prove the chain rule
• prove that exp differentiates to itself
• prove the product rule
• prove the "inverse function theorem" as my course called it:
• prove that log differentiates to 1/x
• put it all together

especially since each individual bit is standard bookwork.
5. (Original post by Smaug123)
...
Well yes, but a binomial expansion is also standard textbook, no? As well as being substantially quicker!
6. (Original post by Lord of the Flies)
Well yes, but a binomial expansion is also standard textbook, no? As well as being substantially quicker!
This is true, but embarrassingly enough it didn't occur to me to carry one out…

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