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 ax is ln(a)*ax 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 ax from first principles, but I got stuck.
From lim h->0 ((ax+h - ax)/h) i got: ax lim h->0 ((ah - 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 ah, 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 ((ah - 1)/h)
Thanks
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 ax is ln(a)*ax 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 ax from first principles, but I got stuck.
From lim h->0 ((ax+h - ax)/h) i got: ax lim h->0 ((ah - 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 ah, 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 ((ah - 1)/h)
Thanks