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Derivative of exponents question HELP

  1. Dec 2, 2011 #1
    1. The problem statement, all variables and given/known data

    find the derivative of: 4e^t((e^2t)-(e^t))

    2. Relevant equations

    d/dx[b^x] = lnb(b^x)d/dx(x)

    3. The attempt at a solution

    I tried subtracting the two exponents in the brackets as well as multiplying it out. both wrong. Help?
     
  2. jcsd
  3. Dec 2, 2011 #2
    Should that read:
    [tex]4e^{t}(e^{2t}-e^{t})[/tex] ?

    You should make it easier on yourself and distribute that [itex]4e^{t}[/itex] through the parenthesis and then take the derivative. Remember to use the chainrule, for example, recall that:
    [tex]\frac{d}{dx}e^{f(x)}=e^{f(x)}\frac{df(x)}{dx}[/tex]
     
  4. Dec 2, 2011 #3

    Mentallic

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    Homework Helper

    So just to be clear, you are trying to find

    [tex]\frac{d}{dt}\left(4e^t\left(e^{2t}-e^t\right)\right)[/tex]

    Correct?

    [tex]e^{2t}-e^t\neq e^t[/tex]

    if that's what you were implying. Remember the rules for subtracting indices are

    [tex]\frac{a^b}{a^c}=a^{b-c}[/tex]

    When you multiplied the factor out (expanded) what did you get?
     
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