Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By skeeter
  • 1 Post By skeeter

Math Help - Derivative of natural log

  1. #1
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Derivative of natural log

    f(x)=ln(x^3-6)^7

    My professor got

    f'(x)=\frac{21x^2}{x^3-6}

    I have

    f'(x)=\frac{21x^2ln(x^3-6)^6}{x^3-6}

    I don't see how my answer is incorrect
    Last edited by amthomasjr; October 31st 2012 at 02:31 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,130
    Thanks
    1012

    Re: Derivative of natural log

    note the power rule for logs ...

    \ln{a^b} = b\ln{a}

    f(x) = \ln(x^3-6)^7 = 7\ln(x^3-6)

    f'(x) = 7 \cdot \frac{3x^2}{x^3-6}
    Thanks from amthomasjr
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Derivative of natural log

    I thought that, but wouldn't the parentheses make a difference?

    ln(a^b)=bln(a)

    but ln(a)^b\neq bln(a)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,130
    Thanks
    1012

    Re: Derivative of natural log

    no, it's the argument (x^3+6) that is raised to the 7th power, not the entire log function ... if that were the case, the function would be written [\ln(x^3+6)]^7 or the more archaic \ln^7(x^3+6)
    Thanks from amthomasjr
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Derivative of natural log

    I see. I've always thought that [ln(x^3-6)]^7 was implied when you write it as ln(x^3-6)^7. Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Natural Derivative
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 14th 2009, 12:27 PM
  2. Derivative of Natural Log
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 28th 2009, 03:45 PM
  3. first derivative with natural log
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 9th 2008, 04:43 PM
  4. Derivative of a Natural Log
    Posted in the Calculus Forum
    Replies: 11
    Last Post: April 20th 2008, 01:52 PM
  5. Derivative of Natural Log
    Posted in the Calculus Forum
    Replies: 16
    Last Post: March 15th 2007, 07:24 PM

Search Tags


/mathhelpforum @mathhelpforum