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Y = x^6.6^x find y' I used a^x = e^(ln a.x)

  1. Apr 24, 2012 #1
    I have a few questions for a quiz
    The question was y = x^6.6^x
    find y'
    I used
    a^x = e^(ln a.x)
    therefore obtained my answer:

    (7x^5)(e^ln( 6 x ))
     
  2. jcsd
  3. Apr 24, 2012 #2
    Re: Intergration/Differentation

    Are you asking what the derivative of
    [tex]x^{6.6^x}[/tex]
    is with respect to x?
     
  4. Apr 24, 2012 #3
    Re: Intergration/Differentation

    i am asking what the derivative of
    (x^6) times (6^x)
    with respect to x
     
  5. Apr 24, 2012 #4
    Re: Intergration/Differentation

    How did you get your answer? It's not right.
     
  6. Apr 24, 2012 #5
    Re: Intergration/Differentation

    i know its not right i got it by using
    a^x = e^(ln a.x)
    and then simplying my answer
     
  7. Apr 24, 2012 #6

    Mark44

    Staff: Mentor

    Re: Intergration/Differentation

    Did you use the product rule? It's easier to see where you went wrong if you show what you did.
     
  8. Apr 24, 2012 #7
    Re: Intergration/Differentation

    yes I did
     
  9. Apr 24, 2012 #8
    Re: Intergration/Differentation

    Are you saying

    [tex]a^x = e^{xln(a)}[/tex]
    ?

    That's certainly true. So we have determined that isn't the cause of your error. What else did you do?
     
  10. Apr 24, 2012 #9
    Re: Intergration/Differentation

    Yes thats what im saying
    i then used the product rule and got
    6x5×eln6x + x6×6/6x×eln6x
     
  11. Apr 25, 2012 #10

    sharks

    User Avatar
    Gold Member

    Re: Intergration/Differentation

    Use LaTex. It's much clearer to display equations.
     
  12. Apr 25, 2012 #11

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Intergration/Differentation

    Please don't use "x" as a variable and to indicate multiplication!
     
  13. Apr 25, 2012 #12

    sharks

    User Avatar
    Gold Member

    Re: Intergration/Differentation

    You could also make a screenshot or take a clear picture of the problem and attach it to your post. Your current problem formatting is confusing, at best.
     
  14. Apr 25, 2012 #13
    Re: Intergration/Differentation

    If I'm going to use the order of operations, taught in elementary school, your answer is

    [tex]6x^5e^{xln(6)}+x^7e^{xln(6)}[/tex]

    Is that what you were trying to write? Of course it wasn't. It was probably closer to

    [tex]6x^5e^{xln(6)}+x^6\frac{6}{6x}e^{xln(6)}[/tex]

    which would result in your incorrect answer given previously. I am assuming you think

    [tex]\frac{d \left (e^{xln(6)} \right )}{dx} = \frac{6}{6x}e^{xln(6)}[/tex]

    That is where you are having your problems. Can you tell me what is the derivative of

    [tex]e^{ax}[/tex]

    where a is just a constant?
     
  15. Apr 26, 2012 #14
    Re: Intergration/Differentation

    Im sorry I am only new to this and did not know how to enter the function correctly.
    I found what I was doing wrong but thanks for the help :)
     
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