Hi

I'm new to this place so I guess I should say I'm from NZ and in first year of university. I'm not actually doing maths this year, but I did university-level maths during my last year of high school (so just assume I have the knowledge of a university first-year student), and maths is still something of intense interest.

So, to the problem: I know that the derivative of a^{x}is ln(a)*a^{x}but I wanted to try work it out from first principles

I've tried searching the internet for answers, but nothing has come up. So I was trying to differentiate a^{x}from first principles, but I got stuck.

From lim h->0 ((a^{x+h}- a^{x})/h) i got: a^{x }lim h->0 ((a^{h}- 1)/h) but I couldn't get any further. You end up with a '0/0' situation which if I remember correctly, you can use L'Hopital's rule, but since it has a^{h}, the derivative of which is what I'm originally trying to work out, that doesn't seem to work.

So, my question is: how do I work out lim h->0 ((a^{h}- 1)/h)

Thanks

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