Proof of the derivative of log x

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Prove that d/dx log a (x) = 1/xlna by using the first principle.
Proof of the derivative of log x to the base a by using the first principle.

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Thank you so much!!
I was looking at khan Academy's proof for the derivative of ln x, to try and find the derivative of log x on my own, but I got stuck :/ I completely forgot about changing bases, you've really helped me a lot😌🙏

noashaham