Differentiation of problems and the Planck function

a)

i) Express the frequency v of electromagnetic radiation as a function of
its wavelength λ and the speed of light c.

ii) By differentiating the frequency with respect to wavelength, show
that the relationship between small increments of frequency Δν and a
small increment of wavelength Δλ can be written



What is the significance of the minus sign?

b) By differentiating the Planck function,



Show that,



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ng the result for part b show that the Planck function Bv has a maximum
or minimum at v = 2.821 kT/h. (you are not expected to demonstrate
which extreme it is; it is in fact a maximum)

Notes to OTA

(I think for the product rule I need to define u = 2hv3/c2 and v =
1/(exp(hv/kT)-1

And for the chain rule I think I need to define w = exp(hv/kT)-1 ???

Am I right in think this?