Understanding the Differentiation of the Cos Law Equation

[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
(1/2)(a- bcos(\theta)^{1/2}(-1)(-bsin(\theta)]<br /> which gives what you say.