Derive group velocity formula in terms of wavelength

[onaboat]

Homework Statement

Starting from: vg=vp+k(dvp/dk) show that the group velocity can also be expressed by vg=vp-λ(dvp/dλ).

Homework Equations

I'm told that vg=vp+k(dvp/dk) with vg=group velocity and vp=phase velocity. I also know that k=(2π)/λ and ω=2πf.

The Attempt at a Solution

I tried to start with the equation ω=kvp and take the derivative with respect to λ but it doesn't work out.

 

[Redbelly98]

(Moved to Advanced Physics.)

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What rule from calculus would allow you to relate

dv_p/dk & dv_p/dλ?