Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By SlipEternal

Thread: The derivative of sin(x)

  1. #1
    May 2011

    The derivative of sin(x)

    The difference quotient is:

    \frac{d}{dx}sin(x) = \lim \Delta x\rightarrow 0=\frac{sin(x+\Delta x)-sin(x)}{\Delta x}

    which converts to:

    =\lim \Delta x\rightarrow 0\frac{sin(x)cos\Delta x+cos(x)sin(\Delta x)-sin(x)}{\Delta x}

    The above I understand. The below step is supposed to be an algebraic rearrangement of the above:

    \frac{d}{dx}sin(x)=\lim \Delta x\rightarrow 0[cos(x)(\frac{sin(\Delta x)}{\Delta x})-sin(x)(\frac{1-cos(\Delta x)}{\Delta x})]

    I am wondering how things were changed to the step above. I am not seeing it right now.

    Thanks in advance...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Nov 2010

    Re: The derivative of sin(x)

    \dfrac{ab+cd}{e} = a\dfrac{b}{e} + c\dfrac{d}{e} = \dfrac{ab}{e} + \dfrac{cd}{e} (this is order of operations and associativity of multiplication). Apply that to what you had. Consider the terms of the numerator. The first and last term have \sin(x). Factor it from those terms, and you get \sin(x)(\cos(\Delta x)-1). Put a negative sign in front, and you get -\sin(x)(1-\cos(\Delta x)). The middle term has a \cos(x).
    Thanks from sepoto
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lie Derivative (directional derivative proof)
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 28th 2012, 05:42 AM
  2. Replies: 4
    Last Post: October 17th 2012, 06:51 AM
  3. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 02:37 AM
  4. Replies: 0
    Last Post: January 24th 2011, 11:40 AM
  5. Replies: 2
    Last Post: November 6th 2009, 02:51 PM

Search Tags

/mathhelpforum @mathhelpforum