The number density of photons left over from the Big Bang has an energy dependence of the form n(E) = E²/(eᴱ¹ᵀ-1), where E is the energy of the photon and T is the temperature of this relic radiation. (For your information, this temperature has been measured to be about -270°C, but don’t use this information for the questions below.)
a). In order to see how this number density changes with energy, we need the derivative of n(E) with respect to e keeping t fixed. Evaluate dn/dE at fixed T and enter it below.