Proving the Relationship Between \omega, \lambda and c

[mrausum]

Homework Statement

Show that:

$$\frac{dc}{d\omega}=\frac{1}{k}\left(1-\frac{c}{v_{g}}\right)$$

The Attempt at a Solution

$$\frac{dc}{d\omega}=\frac{dc}{d\omega}\frac{d\omega}{d\omega}=\frac{dc}{d\omega}\frac{dck}{d\omega}=\frac{dc}{d\omega}k+\frac{dk}{d\omega}c=\frac{dc}{d\omega}k+\frac{c}{v_{g}}=\left\frac{1}{1-k}\right\frac{c}{v_{g}}$$

...Yeah, I have no clue. $$\omega$$, $$\lambda$$ and c are all functions of each other, and I'm confused :(.

 

[mrausum]

Nevermind, solved it. I was really close, I just made a stupid mistake with my algebra.