Results 1 to 7 of 7

Math Help - Derivative of a log function

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    67

    Derivative of a log function

    Normally I would know how to get a simple log derivative, but this problem is much more difficult.

    ln \frac{x^2\sqrt{4x+1}}{(x^3+5)^3}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jul 2009
    Posts
    152
    Quote Originally Posted by radioheadfan View Post
    Normally I would know how to get a simple log derivative, but this problem is much more difficult.

    ln \frac{x^2\sqrt{4x+1}}{(x^3+5)^3}
    Let g(x)= \ln f(x) represent the given fuction. The derivitive is then [1/f(x)]\cdot f^\prime (x). Use the Quotient Rule or Product Rule for the last bit.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by radioheadfan View Post
    Normally I would know how to get a simple log derivative, but this problem is much more difficult.

    ln \frac{x^2\sqrt{4x+1}}{(x^3+5)^3}
    Use the usual log rules to get an expression that is simpler to differentiate.


    Edit: By the way, you better note that \ln x^2 = 2 \ln |x|.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jul 2009
    Posts
    152
    Quote Originally Posted by mr fantastic View Post
    Use the usual log rules to get an expression that is simpler to differentiate.
    Or that...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2009
    Posts
    67
    I used the log rules and got 2/3
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by radioheadfan View Post
    I used the log rules and got 2/3
    What happened to all the x's?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Jul 2009
    Posts
    152
    Quote Originally Posted by radioheadfan View Post
    I used the log rules and got 2/3
    Don't think that's right...

    Using the log rules, we get

    \ln x^2 + \ln\sqrt{4x+1} - \ln[(x^3+5)^3]

    =2\ln|x| +\frac{1}{2}\ln(4x+1) -3\ln(x^3+5).

    Now differentiate...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of a function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 24th 2011, 06:48 PM
  2. [SOLVED] Derivative of this function?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2010, 11:02 PM
  3. function --- derivative (help!)
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 23rd 2010, 01:47 PM
  4. derivative of a function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2010, 01:30 AM
  5. the derivative function
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 21st 2010, 07:56 AM

Search Tags


/mathhelpforum @mathhelpforum