1. Jun 4, 2012 #1

   V0ODO0CH1LD

   

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

    

   V0ODO0CH1LD, Jun 4, 2012
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3. Jun 4, 2012 #2

   micromass

   

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   An example of what you're trying to do would be welcome.

    

   micromass, Jun 4, 2012
4. Jun 4, 2012 #3

   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##.

    

   theorem4.5.9, Jun 4, 2012
5. Jun 4, 2012 #4

   V0ODO0CH1LD

   

   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)"?

    

   V0ODO0CH1LD, Jun 4, 2012

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