The simple derivative really is nice, thanks for pointing this out!

Your explanation makes a lot of sense to me! I didn’t know that exp'(x) = exp(x), but can see how this could be an interesting property and in turn makes ln interesting.

You saying, that it often doesn’t matter which logarithm is used, made me check and realize that log_a(x)/log_a(y) is the same as log_b(x)/log_b(y). Thus I understand that it really doesn’t make a difference which logarithm is used when “comparing the magnitude” (not sure if this is the right term) of numbers.

I feel like I have a much better understanding of ln now. I’ll assume that the base of an algorithm is often basically a random choice and base e is often used because of its “interesting trivia”.

Thanks a lot!