Results 1 to 15 of 15

Math Help - derivitive

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    13

    derivitive

    take derivitive:

    y=arcsin(2t)^(1/2)


    Moderator edit: Also asked here: http://www.mathhelpforum.com/math-he...erivative.html
    Last edited by mr fantastic; November 17th 2009 at 06:13 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Use the derivative of the inverse sine function:

    \frac{d(sin^{-1}x)}{dx}=\frac{1}{\sqrt{1-x^{2}}};

    as well as the chain rule.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    13
    Can you show a step by step solution.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Theres really only two steps here. You're just plug and chugging. What is X in this case? What is The derivative of X. What does the chain rule say to do. Answer those questions first, and if your answers are incorrect I will do the steps.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    13
    the x is sqrt(2t), and the chain rule is the derivative multiplied by the inside multplied by the derivative of the inside
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2009
    Posts
    13
    the derivative of x is 1/sqrt(2t)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Ok awesome. So now multiply the derivative of the "X" you just calculated, by the derivative of the sine inverse function, making sure to substitute your "X" into the portion marked x-squared.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Nov 2009
    Posts
    13
    What is the end solution, so that we can compare?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    What did you get and I can let you know if you did it right or not.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Nov 2009
    Posts
    13
    1/(sqrt(2)sqrt(t-2t^2))
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Hmm. Not quite.

    \frac{d(sin^{-1}\sqrt{2t})}{dx}=\frac{2}{2\sqrt{2t}}*\frac{1}{\s  qrt{1-(\sqrt{2t})^{2}}}
    \frac{d(sin^{-1}\sqrt{2t})}{dx}=\frac{1}{\sqrt{2t}\sqrt{1-2t}}

    Remember that:

    (\sqrt{x})^{2}=x
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Nov 2009
    Posts
    2
    I have the same problem. The answer that you gave is not the answer that came from our book. And I cannot make the connection between the two. The answer given was sqrt2/sqrt(1-2t^2).
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Quote Originally Posted by 10colbathb View Post
    I have the same problem. The answer that you gave is not the answer that came from our book. And I cannot make the connection between the two. The answer given was sqrt2/sqrt(1-2t^2).
    The answer in the book is not possible.

    EDIT: Please check. Is the problem:

    \frac{d(sin^{-1}(\sqrt{2t})}{dx}

    Or -

    \frac{d(sin^{-1}(\sqrt{2}*t)}{dx}
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Newbie
    Joined
    Nov 2009
    Posts
    2
    The problem originally stated is the correct one.
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Quote Originally Posted by 10colbathb View Post
    The problem originally stated is the correct one.
    There is an error in your book then. In the radicand of our derivative:

    (\sqrt{2t})^2\neq2t^{2}

    And the derivative of the argument inside the sine inverse, does not produce a \sqrt{2} in the numerator, even after rationalizing the \sqrt{2t} in the denominator of both or our problems.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. derivitive help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 1st 2009, 11:47 AM
  2. Derivitive
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 11th 2008, 05:39 PM
  3. Second/Third Derivitive
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 25th 2008, 06:35 PM
  4. Need Derivitive Help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2007, 03:09 PM
  5. second derivitive ..HELP!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 29th 2007, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum