Results 1 to 6 of 6

Math Help - Another Differentiation Problem

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    18

    Another Differentiation Problem

    Find dy/dx for the following curve:

    x = ( 1 - a sq ) to the power of 3/2
    y = sin to the power of -1 ( a )
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    can you confirm the equations

    Looks like,

    x= (1-\sqrt{a})^{\frac{3}{2}}
    y= sin^{-1}(a)
    Last edited by pickslides; June 2nd 2009 at 11:33 PM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by puggie View Post
    Find dy/dx for the following curve:

    x = ( 1 - a sq ) to the power of 3/2
    y = sin to the power of -1 ( a )
    As I said in your last post, this requires Parametric Differentiation.

    Remember, \frac{dy}{dA} \times \frac{dA}{dx} = \frac{dy}{dx}

    Is it differentiating the equations themselves you are struggling with?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2009
    Posts
    18
    Hi pickslides

    y as you have written is correct.

    x should be a square and not square root of a!

    The answer is -1/3a(1-a square)

    Thanks everybody
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    x=(1-a^2)^{\frac{3}{2}}
    y=sin^{-1}(a)

    Substitute a=sin \theta

    y=\theta

    x=(1-sin^2\theta)^{\frac{3}{2}}

    x=cos^3\theta

    \frac{dx}{d\theta}=3cos^2\theta*-sin\theta
    \frac{dx}{dy}=3cos^2\theta*-sin\theta
    \frac{dx}{dy}=3(1-a^2)*-a
    \frac{dx}{dy}=3a(a^2-1)
    \frac{dy}{dx}=\frac{1}{3a(a^2-1)}
    Last edited by alexmahone; June 3rd 2009 at 10:11 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    x= (1-a^2)^{\frac{3}{2}}

    from this find \frac{dx}{da}

    y= sin^{-1}(a)

    from this find \frac{dy}{da}

     then \frac{dy}{dx} = \frac{dy}{da} \times \frac{1}{\frac{dx}{da}}<br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem concerning differentiation
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 14th 2009, 04:15 PM
  2. Differentiation problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 1st 2009, 08:18 AM
  3. Differentiation Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2009, 08:55 AM
  4. Differentiation problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 2nd 2008, 08:15 PM
  5. Differentiation Problem!!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 2nd 2008, 05:32 AM

Search Tags


/mathhelpforum @mathhelpforum