Results 1 to 3 of 3

Math Help - derivative of arctan^3

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    162

    derivative of arctan^3

    I have a question with finding the derivative of the function below:

    y= arctan^3(\frac{x}{ln(x)}).

    This is what I get when I take the derivative of the function:



    \frac{d}{dx} 3(sec^2y)(tan^2y) = \frac{ln(x)-1}{(lnx)^2}

    I don't know how to solve for (sec^2y)(tan^2y) in terms of x. I cannot figure out how. I know it is dealing with sin^2y+cos^2y=1 and dividing by either sin^2y or cos^2y depending on what you want. But I don't see how you can get a polynomial out of that.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093

    Re: derivative of arctan^3

     y = \left( \tan ^{-1} \left(\frac{x}{\ln (x)}\right)\right)^3

     y^{\frac{1}{3}} = \tan ^{-1} \left(\frac{x}{\ln (x)}\right)

    \tan (y^{\frac{1}{3}}) = \frac{x}{\ln (x)}

    now derive

    you did something wrong since you considered

     \tan ^3 (y) = \frac{x}{\ln (x)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    162

    Re: derivative of arctan^3

    Thanks, I looked it over today and I got the right answer. Thanks bud.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of arctan in a partial derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 12th 2010, 01:52 PM
  2. Derivative of arctan...
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 28th 2010, 04:14 PM
  3. Derivative of Arctan
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 20th 2010, 01:56 AM
  4. derivative of arctan
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 1st 2009, 05:29 PM
  5. Derivative of arctan(x/y)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 15th 2009, 03:27 PM

Search Tags


/mathhelpforum @mathhelpforum