# Diferentiating cos law

1. Apr 17, 2012

### 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

Last edited: Apr 17, 2012
2. Apr 17, 2012

### mholland

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

3. Apr 17, 2012

### HallsofIvy

Staff Emeritus
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)][tex]
which gives what you say.