Derivative of Exponential Functions with Other Logs

  • #1
V0ODO0CH1LD
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Can the derivative of an exponential function be calculated with logs base something other than e? Like base 10 or 2?
 

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  • #2
micromass
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An example of what you're trying to do would be welcome.
 
  • #3
theorem4.5.9
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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##.
 
  • #4
V0ODO0CH1LD
278
0
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)"?
 

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