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Diferentiating cos law

  1. Apr 17, 2012 #1
    I'm struggling here as i've not done diferentiation in a few years.
    The cos law states:
    c=(a2+b2-2abcosθ)1/2

    I'm trying to figure out how to differentiate this, so if c were a length, what the velocity with which c grows as θ increases (ie c dot)

    Any pointers would be great!!

    If its easier, a and b are fixed lengths, so the equation simplifies to
    c=(a-bcosθ)1/2
     
    Last edited: Apr 17, 2012
  2. jcsd
  3. Apr 17, 2012 #2
    is it just
    c dot=0.5(a-bcosθ)-1/2.(bsinθ) ?
     
  4. Apr 17, 2012 #3

    HallsofIvy

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    Yes, it's just an application of the basic differentiation laws, particularly the chain rule.

    The deriviative of [itex]u^{1/2}[/itex], with respect to u, is [itex](1/2)u^{-1/2}[/itex]. The derivative of 1- v, with respect to v is -1, and, finally, the derivative of [itex]bcos(\theta)[/itex], with respect to [itex]\theta[/itex], is [itex]-bsin(\theta)[/itex].

    Putting those together, using the chain rule, the derivative of c is
    [tex](1/2)(a- bcos(\theta)^{1/2}(-1)(-bsin(\theta)][tex]
    which gives what you say.
     
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