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Homework Help: Exponential function and chain rule - find derivative

  1. May 15, 2013 #1
    1. The problem statement, all variables and given/known data
    If [itex] f(x) = e^{3x^2+x} [/itex], find f'(2)

    2. Relevant equations
    [itex]f'(x) = a^{g(x)}ln a g'(x)[/itex]

    3. The attempt at a solution
    [itex] f'(x) = (e^{3x^2+x})(ln e)(6x+1)[/itex]
    [itex] f'(2) = (e^{3(2)^2+2})(ln e)(6(2)+1) [/itex]
    [itex] = 2115812.288[/itex]

    I was checking online and I'm seeing a different answer, but this is EXACTLY how my lesson is showing how to answer. Is this correct?
  2. jcsd
  3. May 15, 2013 #2


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    Science Advisor
    Homework Helper

    Looks to me like you are getting 13*e^(14). That's ok. But it's not equal to 2115812.288. How did you get that?
  4. May 15, 2013 #3
    Oh I'm not sure how I managed that. Thank you :)
  5. May 15, 2013 #4


    Staff: Mentor

    The exact value of f'(2) is 13e14. If you use a calculator on this, the result is only an approximation.

    BTW, there's no point in writing ln(e), since it is 1 (exactly).
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