1. ## derivative of a^x

i am trying to find the derivative of a^x using the limit definition of the derivative.

in order to find the derivative of a^x i need to show:
lim (a^h - 1) / h = ln(a)
h~>0

i can't see any obvious way to manipulate the expression so that i get ln a in the end. please help.

2. Originally Posted by oblixps
i am trying to find the derivative of a^x using the limit definition of the derivative.

in order to find the derivative of a^x i need to show:
lim (a^h - 1) / h = ln(a)
h~>0

i can't see any obvious way to manipulate the expression so that i get ln a in the end. please help.
You will struggle using this approach I think. Read section 3 and 4 here: http://www.mash.dept.shef.ac.uk/Reso...b-logs-exp.pdf

3. Originally Posted by mr fantastic
You will struggle using this approach I think. Read section 3 and 4 here: http://www.mash.dept.shef.ac.uk/Reso...b-logs-exp.pdf
thanks! is there any way to do that limit algebraically though?

4. Originally Posted by oblixps
thanks! is there any way to do that limit algebraically though?
Not without knowing what the derivative of a^x is ....!