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First principles differentiation question

  1. Nov 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Obtain the derivative of [tex]e^{2x}[/tex] from first principles.

    2. Relevant equations

    3. The attempt at a solution
    I am upto the point where i have [tex]e^{2x}(\frac{e^{2h}-1}{h})[/tex] Where LIM h->0.

    I just don't see how 2 is obtained from what's in the ().
  2. jcsd
  3. Nov 4, 2007 #2


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    Science Advisor

    [tex]\frac{e^{2h}-1}{h}= 2\frac{e^{2h}-1}{2h}= 2\frac{e^u -1}{u}[/tex]
    if you let u= 2x.

    Now, do you know what the limit, as u goes to 0 of
    [tex]\frac{e^u- 1}{u}[/tex]
  4. Nov 4, 2007 #3
    It tends to 1? I think i understand this now, thanks very much for your help.
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