Results 1 to 3 of 3

Math Help - Differential of dy

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Question Differential of dy

    a)find the differential dy of the function y(x)=x√(1-x^2)

    defined for x in (-1,1)

    B) for the function y(x)=x√(1-x^2) use the result in a) to find dy when x=0.0 and dx=0.01. Compare the value with delta y for x=0.0 and dx=0.01
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: Differential of dy

    Quote Originally Posted by LAPOSH42 View Post
    a)find the differential dy of the function y(x)=x√(1-x^2)

    defined for x in (-1,1)

    B) for the function y(x)=x√(1-x^2) use the result in a) to find dy when x=0.0 and dx=0.01. Compare the value with delta y for x=0.0 and dx=0.01
    Assuming that you meant you want to find the derivative

    \displaystyle \begin{align*} y &= x\sqrt{1-x^2} \\ y^2 &= x^2(1 - x^2) \\ y^2 &= x^2 - x^4 \\ \frac{d}{dx}\left(y^2\right) &= \frac{d}{dx}\left(x^2 - x^4\right) \\ 2y\,\frac{dy}{dx} &= 2x - 4x^3 \\ \frac{dy}{dx} &= \frac{2x - 4x^3}{2y} \\ \frac{dy}{dx} &= \frac{x - 2x^3}{y} \\ \frac{dy}{dx} &= \frac{x - 2x^3}{x\sqrt{1 - x^2}} \\ \frac{dy}{dx} &= \frac{1 - 2x^2}{\sqrt{1 - x^2}}  \end{align*}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2011
    Posts
    14

    Thumbs up Re: Differential of dy

    thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 8th 2011, 01:27 PM
  2. 'Differential' in differential equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 5th 2010, 11:20 AM
  3. Double differential / differential squared
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 04:51 PM
  4. Replies: 2
    Last Post: May 18th 2009, 04:49 AM
  5. Differential
    Posted in the Calculus Forum
    Replies: 34
    Last Post: March 26th 2007, 07:57 PM

Search Tags


/mathhelpforum @mathhelpforum