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Difficult derivative involving vectors and trig

  1. Oct 5, 2012 #1
    Hello,

    I am working through some very old (1980's) computer code and need to understand how a particular derivative was calculated. Can someone explain to me how it is that if:

    [itex]\vec{a}=\vec{f}\times\vec{g}[/itex]
    [itex]\vec{b}=\vec{h}\times\vec{g}[/itex]

    and

    [itex]sin(\phi)=\frac{\left|\vec{a}\times\vec{b}\right|}{\left|a\right|\left|b\right|}[/itex]
    [itex]cos(\phi)=\frac{\vec{a}\cdot\vec{b}}{\left|a\right|\left|b\right|}[/itex]

    then:

    [itex]\frac{d\phi}{d\vec{f}} = -\frac{\left|g\right|}{\left|a\right|^2}\cdot\vec{a}[/itex]?

    I would very much appreciate any help with this!

    Thanks :)
     
  2. jcsd
  3. Oct 6, 2012 #2

    haruspex

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    Have you tried differentiating sin phi wrt f?
     
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