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Derivative of Exponential Functions with Other Logs

  1. Jun 4, 2012 #1
    Can the derivative of an exponential function be calculated with logs base something other than e? Like base 10 or 2?
     
  2. jcsd
  3. Jun 4, 2012 #2

    micromass

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    An example of what you're trying to do would be welcome.
     
  4. Jun 4, 2012 #3
    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##.
     
  5. Jun 4, 2012 #4
    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)"?
     
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