# Derivative of Exponential Functions with Other Logs

V0ODO0CH1LD
Can the derivative of an exponential function be calculated with logs base something other than e? Like base 10 or 2?

## Answers and Replies

Staff Emeritus
Homework Helper
An example of what you're trying to do would be welcome.

theorem4.5.9
You can, but you will get an extra constant from the chain rule. Just use a change of base formula for log or rewrite an exponential in some other base and the term comes right out.

##e## is important precisely because it's the only base of the exponential where after differentiating the constant is ##1##.

V0ODO0CH1LD
You can, but you will get an extra constant from the chain rule. Just use a change of base formula for log or rewrite an exponential in some other base and the term comes right out.

##e## is important precisely because it's the only base of the exponential where after differentiating the constant is ##1##.

Could you maybe expand on that? Or point out somewhere where I could read about it?

If I start with "f(x+Δx) - f(x) = a^(x+Δx) - a^x" how do I continue with log_2 or anything else from here? Would I even go to that being equal to "a^x * (a^Δx - 1)"?