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Derivative of e^x=e^x, the derivative of e^2x doesn't equal e^2x

  1. Mar 14, 2007 #1
    I have a test tomorrow so I may keep asking questions frequently. For now, why is it that when the derivative of e^x=e^x, the derivative of e^2x doesn't equal e^2x. I've been looking for the rule but can't find it anywhere.
     
  2. jcsd
  3. Mar 14, 2007 #2

    cristo

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    Use the chain rule.
     
  4. Mar 14, 2007 #3
    derivative of
    e^x = (1)(e^x)
    the 1 comes from the derivative of x because of chain rule

    derivative of
    e^2x = (2)(e^2x)
    the 2 comes from the derivative of 2x because of chain rule

    correct me if i am wrong.
     
    Last edited: Mar 14, 2007
  5. Mar 14, 2007 #4
    thanx, makes much more sense
     
  6. Mar 14, 2007 #5

    mathwonk

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    learn this rule: d/dx(e^u) = e^u (du/dx)
     
  7. Mar 15, 2007 #6
    [tex] e^{2x}=[e^x]^2 [/tex]
    Since [tex]\frac{d}{dx}f(x)^n = nf'(x){f(x)}^{n-1}[/tex]
    then if [tex]f(x)=e^{2x}[/tex] ...go from there.
     
  8. Mar 15, 2007 #7

    HallsofIvy

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    That's again the chain rule but with the two functions reversed!
     
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