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

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  • #1
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Main Question or Discussion Point

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.
 

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  • #2
cristo
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Use the chain rule.
 
  • #3
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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:
  • #4
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thanx, makes much more sense
 
  • #5
mathwonk
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learn this rule: d/dx(e^u) = e^u (du/dx)
 
  • #6
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[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.
 
  • #7
HallsofIvy
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That's again the chain rule but with the two functions reversed!
 

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