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Derivatives of exponentials (calc II)

  1. Aug 31, 2011 #1
    1. The problem statement, all variables and given/known data
    [tex]\frac{d}{dx}e^{ax^{3}}[/tex]

    I'm simply trying to determine whether or not I am doing these correctly and applying the chain rule properly.
    2. Relevant equations
    Chain rule et al.

    3. The attempt at a solution

    [itex]\frac{d}{dx}e^{ax^{3}}[/itex]

    [itex]e^{ax^{3}}\frac{d}{dx}ax^{3}[/itex]

    [itex]e^{ax^{3}}a(3)x^{2}[/itex]

    [itex]3ae^{ax^{3}}x^{2}[/itex]

    Does that look right to you? I am assuming "a" is just some constant, the book does not specify.
     
  2. jcsd
  3. Aug 31, 2011 #2

    vela

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    Looks fine.
     
  4. Aug 31, 2011 #3
    Yes, this is correct. If you'd like proof take a look at (http://www.wolframalpha.com/input/?i=derivative+of+e^%28ax^3%29). "wolframalpha.com"[/URL] is a very good resource for checking your answers. Good luck!
     
    Last edited by a moderator: Apr 26, 2017
  5. Aug 31, 2011 #4
    Okay great!

    How about this one?

    [itex]\frac{d}{dt}e^{tsin(2t)}[/itex]

    [itex]e^{tsin(2t)}\frac{d}{dt}tsin(2t)[/itex]

    [itex]e^{tsin(2t)}[sin(2t)+2cos(2t)][/itex]
     
  6. Aug 31, 2011 #5

    vela

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    Almost. The last term isn't correct.
     
  7. Aug 31, 2011 #6
    Oh I think I just didn't type the "t". It's on my paper.

    [itex]e^{tsin(2t)}[sin(2t)+2tcos(2t)][/itex]

    Better?
     
  8. Aug 31, 2011 #7

    vela

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    Ayuh.
     
  9. Aug 31, 2011 #8
    Thanks a bunch!
     
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