How do you change Planck's law from frequency to wavelength?
I have to derive Wien's displacement law by using Planck's law. I've tried but I come to a unsolvable equation (well I can't solve it) anywhere I look online it comes to the same conclusion, you need to solve an equation involving transcendentals which I have no idea what they are nor any of the math classes required for this physics course teach it. Once that equation is solved, the next steps are quite simple, by using the solution.
Maybe my professor just wants us to google the solution to the equation and used it to keep solving the problem?
anyway, what really bothers me is this:
My book shows Planck's law in terms of frequency
but to do the problem I need it in terms of wavelength
And , so by that then it can be said that the exponent of would be 3 when it is expressed in terms of lambda (plus would have an exponent of 1). But Wikipedia says it is 5 and not 3. It multiplies by the derivative of , but I don't get why. I'm just substituting, not differentiating, no need to use the chain rule.