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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 :)

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# Difficult derivative involving vectors and trig

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