e^{-\beta\hbar\omega_s({\bf k})}(-\hbar\omega_s({\bf k}))}
{(1-e^{-\beta\hbar\omega_s({\bf k})})^2}\nonumber\\
&=&-\frac{1}{V}\sum_{{\bf k}s}\hbar\omega_s({\bf k})
e^{-\beta\hbar\omega_s({\bf k})}(-\hbar\omega_s({\bf k}))}
{(1-e^{-\beta\hbar\omega_s({\bf k})})^2}\nonumber\\
&=&-\frac{1}{V}\sum_{{\bf k}s}\hbar\omega_s({\bf k})