posted by bob on .
E^2/(e^(E/T)-1)Evaluate dn/dE at fixed T and enter it below.
Is E^2/(e^(E/T)-1) the function n(E,T) that you want to differentiate?
Is E = h*f/k where f is a frequency, h = Planck's constant and k is Boltzmann's contant? The dimensions of E and T must be the same.
It looks like you are trying to derive the formula for the peak frequency of the Planck blackbody function.
In any case, just use the rule for dfferentiating the derivative of the ratio of two functions.
d/dx (f(x)/g(x)) = [g(df/dx - f*dg/dx]/g^2
In your case, x = E, f(E) = E^2 and g(E) = e^(E/T) -1