Results 1 to 7 of 7

Math Help - Trig Differentiation

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    14

    Trig Differentiation

    cos x
    square root x

    the derivative of this, i just need a worked example, i just keep getting the wrong answer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2008
    Posts
    91
    using the quotient rule  \frac {d} {dx} \frac {cosx} {\sqrt{x}} = \frac {-sinx \sqrt{x} - \frac {1} {2} cosx \frac {1} {\sqrt{x}}  } {x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    14
    yes i got to there but the answer takes it further, like it has a denominator of 2x ROOT x in the answers, anyway to go furhter than that?

    thanks anyway
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2008
    From
    Montreal
    Posts
    311
    Awards
    1
    \frac{\cos(x)}{\sqrt{x}} = \frac{\cos(x)}{x^{1/2}} = \cos(x) \cdot x^{-1/2} which should simplify the calculation

    so once we differentiate we get:

    -\sin(x) \cdot x^{-1/2} +\left(-\frac{1}{2}x^{(-1/2-1)} \cdot \cos(x) \right)

    simplifying we have:

    \frac{\sin(x)}{x^{1/2}} -\frac{\cos(x)}{2 x^{3/2}}

    \frac{2x\cdot \sin(x)- \cos(x)}{2x^{3/2}}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by I Drink and Derive View Post
    cos x
    square root x

    the derivative of this, i just need a worked example, i just keep getting the wrong answer
    I would use the quotient rule which for \frac{u}{v} is:

    y\prime = (vu\prime - uv\prime)/v^2

    Let u = \cos{x} and v = \sqrt{x} so that u\prime = -\sin{x} and v\prime = \frac{1}{2}x^{-1/2}

    Putting these together we get y\prime = (-\sqrt{x}\sin{x} - \frac{x^{-1/2}}{2}\cos{x})/{x}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by nmatthies1 View Post
    using the quotient rule  \frac {d} {dx} \frac {cosx} {\sqrt{x}} = \frac {-sinx \sqrt{x} - \frac {1} {2} cosx \frac {1} {\sqrt{x}} } {x}
    Quote Originally Posted by I Drink and Derive View Post
    yes i got to there but the answer takes it further, like it has a denominator of 2x ROOT x in the answers, anyway to go furhter than that?

    thanks anyway
    To save people wasting time re-inventing the wheel, it would help if you showed where you got stuck so the that help could be given from that point.

    Multiply the numerator and denominator of this answer by 2 \sqrt{x}.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2008
    Posts
    91
    Quote Originally Posted by nmatthies1 View Post
    using the quotient rule  \frac {d} {dx} \frac {cosx} {\sqrt{x}} = \frac {-sinx \sqrt{x} - \frac {1} {2} cosx \frac {1} {\sqrt{x}} } {x}
    yes at that point it is just simplifying

     \frac {-sinx \sqrt{x} - \frac {1} {2} cosx \frac {1} {\sqrt{x}} } {x} =  \frac {-sinx \sqrt{x}} {x} - \frac {\frac {1} {2} cosx \frac {1} {\sqrt{x}}} {x} =  \frac {-sinx} {\sqrt{x}} - \frac {cosx} {2x \sqrt{x}} =   \frac {-2xsinx-cosx} {2x \sqrt{x}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig differentiation.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 27th 2010, 01:23 PM
  2. Replies: 3
    Last Post: February 21st 2010, 02:04 PM
  3. Simple trig differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 27th 2010, 05:14 PM
  4. trig differentiation
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 4th 2009, 01:49 PM
  5. Implicit differentiation with trig
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 20th 2007, 11:22 PM

Search Tags


/mathhelpforum @mathhelpforum