Results 1 to 3 of 3

Math Help - Derivative

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    43

    Derivative

    Differentiate log(base 7)(4x^2+1)
    Last edited by mr fantastic; October 24th 2009 at 10:33 PM. Reason: Added the instruction from the post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,116
    Thanks
    1000
    Quote Originally Posted by Asuhuman18 View Post
    log(base 7)(4x^2+1)
    \frac{d}{dx} \log_b(u) = \frac{1}{\ln{b}} \cdot \frac{u'}{u}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602
    Quote Originally Posted by Asuhuman18 View Post
    log(base 7)(4x^2+1)
    Use the change of base rule to turn it into a natural logarithm function.


     y = \log_7{(4x^2 + 1)}

     = \frac{\ln{(4x^2 + 1)}}{\ln{7}}

     = \frac{1}{\ln{7}}\cdot\ln{(4x^2 + 1)}.


    Let u = 4x^2 + 1 so that y=  \frac{1}{\ln{7}}\cdot\ln{u}.


    \frac{du}{dx} = 8x


    \frac{dy}{du} = \frac{1}{\ln{7}}\cdot\frac{1}{u}

     = \frac{1}{(4x^2 + 1)\ln{7}}.


    Therefore

    \frac{dy}{dx} = \frac{8x}{(4x^2 + 1)\ln{7}}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 03:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 12:40 PM
  3. Replies: 2
    Last Post: November 6th 2009, 03:51 PM
  4. Replies: 1
    Last Post: January 7th 2009, 02:59 PM
  5. Total Derivative vs. Directional Derivative
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: May 30th 2008, 09:42 AM

Search Tags


/mathhelpforum @mathhelpforum