1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook