Given $$u (\lambda) d\lambda = \frac{8 \pi hc \lambda ^{-5}}{e^{\frac {hc}{\lambda k t}}-1}d\lambda,$$ I want to convert this into frequency form $u(\nu)d \nu$. Basically, I want to covert the amount of energy in a wavelength $\lambda \to \lambda + d\lambda$ to the corresponding expression from $\nu \to \nu + d\nu$. I know that $\nu = \frac{c}{\lambda}$ and to replace this in the denominator, and I know that $d\nu = -\frac{c}{\lambda^2}d\lambda$, but I can't make the formula come out right. What am I missing?

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    $\begingroup$ What did you get? Did you fail on contants or on $d\lambda/\lambda^5 \propto d\nu\nu^3$? $\endgroup$
    – JEB
    Commented Jan 18, 2019 at 0:01
  • $\begingroup$ The latter. Additionally, I'm not sure where the negative sign from the derivative goes. $\endgroup$
    – user206026
    Commented Jan 18, 2019 at 0:05
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/13611/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Jan 18, 2019 at 0:08