Speed of sound is related to the derivative of pressure with respect to density:
$v_s=\sqrt{(\frac{\partial P}{\partial \rho})_S}$
where S tells us the derivative must be taken while keeping entropy constant.
For an ideal Bose gas, $P$ and $\rho$ can be expressed in terms of Bose-Einstein functions:
$g_v(z) = \frac{1}{\Gamma(v)}\int \frac{x^{v-1}}{z^{-1}e^x -1}$
where in the given context $z=e^{\frac{\mu}{T}}$ and $\lambda = \lambda (T)$ is the thermodynamic wavelength
Those expressions are:
$ P = \frac{T}{\lambda^3} g_{\frac{5}{2}}(z)$
$ \rho = \frac{m}{\lambda^3} g_{\frac{3}{2}}(z)$
Having all this in my hands, I still fail to perform the differentiation. Could you please hint what should my first step be?