Differentiating the law of cosines with respect to angle

[mholland]

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

 

[mholland]

is it just
c dot=0.5(a-bcosθ)^-1/2.(bsinθ) ?

 

[HallsofIvy]

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

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

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