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Derivative help of y=cosx!

  1. Oct 14, 2007 #1
    how do you find the derivative of y=cosx by using the limit process of

    limit as h --> 0 is f(x+h) - f(x) / all over h.

    i did this with y=sinx, and the answer was cosx, but i'm having trouble figuring out y=cosx.


    help?
     
  2. jcsd
  3. Oct 14, 2007 #2

    arildno

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    Well,
    [tex]\frac{\cos(x+h)-cos(x)}{h}=\frac{\cos(h)-1}{h}\cos(x)-\frac{\sin(h)}{h}\sin(x)=-\frac{\sin(h)}{h}(\frac{\sin(h)}{\cos(h)+1}\cos(x)+\sin(x))[/tex]
    using well-known identities. Can you finish this?
     
    Last edited: Oct 14, 2007
  4. Oct 14, 2007 #3
    You need to know that

    [tex]\lim_{t\to 0} \frac{\sin(t)}{t}=1.[/tex]

    The most common elementary proof of this is geometric.
     
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