Results 1 to 7 of 7

Math Help - differentiation skills help please!

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    18

    differentiation skills help please!

    I have a formula that I am trying to differentiate, but having lots of problems with it:
    r(s)= (tan^-1 s, root of 2 /2 log(1+s^2), s - tan^-1 s)
    its derivates:
    r'(s) = ( ( 1+s^2)^-1, root of 2 s(1+s^2)^-1, 1- (1+s^2)-1

    = (1+s^2)^-1 (1, root of 2 s, s^2)

    I dont know how the derivative of tan^-1(s) = 1/1+s^2, can anyone explain?

    And cannot follow how all the derivatives work out, can anyone talk me through it? I have exam shortly and ally need to get to know these off by heart.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    We mostly do not worry about deriving these each time. That's why they're memorized or looked up if needed. You can use the triangle to derive the derivative of arctan.

    y=tan^{-1}(x), \;\ x=tan(y)

    Differentiate the right equation implicitly:

    \frac{d}{dx}[x]=\frac{d}{dx}[tan(y)]

    1=sec^{2}(y)\frac{dy}{dx}

    \frac{dy}{dx}=\frac{1}{sec^{2}(y)}=\frac{1}{sec^{2  }(tan^{-1}(x))}.........[1]

    It follows from the triangle that:

    sec^{2}(tan^{-1}(x))=1+x^{2}

    And so, from [1], we have \frac{dy}{dx}=\frac{1}{1+x^{2}}
    Last edited by galactus; November 24th 2008 at 05:38 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    18
    Thanks galactus, much appreciated
    !
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    I recently posted a solution for your problem.

    Double postin' is against the Rules, did you read them?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2007
    Posts
    18
    where exactly did you post it? My problem was for the whole equation, not just the first part. Do you have a link to your post? Or show me how I could have searched for it. If i know hwo to search properly for it, then I will next time.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    You wanted to find (\arctan x)', I posted the solution here.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2007
    Posts
    18
    I se now, yeah sorry for the double post. Can you help with my other question on the board about algebraic simplification?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Skills and Applications
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 12th 2010, 10:10 PM
  2. Algebra Skills and Polynomials
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 6th 2009, 08:34 PM
  3. Trying to strengthen my math skills
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 10th 2009, 02:17 PM
  4. numerical skills and prealgebra help:)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 30th 2008, 05:59 PM
  5. communication skills I don't have
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 5th 2007, 08:03 AM

Search Tags


/mathhelpforum @mathhelpforum