I'm trying to find how to take the derivative of 2^x by use of the difference quotient, rather than simply using derivative rules. I know it's ln(2) * 2^x, but I need to essentially prove it. Does anyone know how?

- Oct 28th 2008, 02:32 AMpantsaregoodFinding the derivative of an exponential using the difference quotient
I'm trying to find how to take the derivative of 2^x by use of the difference quotient, rather than simply using derivative rules. I know it's ln(2) * 2^x, but I need to essentially prove it. Does anyone know how?

- Oct 28th 2008, 04:58 AMtoraj58

so

differntiate two sides of the equation:

left is equat to :

so we have:

then we have:

- Oct 28th 2008, 06:24 AMHallsofIvy
But toraj58's response doesn't address the question: find the integral using the difference quotient; i.e. the basic definition of the derivative.

pantsaregood, the difference quotient for a function f if [f(x+h)- f(x)]/h. What is that when ? You can use one of the laws of exponents to simplify that a little. - Oct 28th 2008, 06:41 PMpantsaregood
2^x

[2^(x+h)-2^x]/h

That really doesn't get me anywhere, though.