Planck Function: Subbing c=λν - Insight Needed

[Piano man]

Expressing Planck's Law as a function of frequency, we have:
$$I(\nu)=\frac{2h\nu^3}{c^2}\frac{1}{e^{\frac{h\nu}{kT}}-1}$$
Expressing this in terms of wavelength, one should get
$$I(\lambda)=\frac{2hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1}$$

but I don't see how this is obvious by subbing in $$c=\lambda \nu$$
Any insights?

Thanks

 

[arkajad]

Remember:

$$|I(\lambda)d\lambda| =|I(\nu)d\nu|$$

and

$$d\lambda=-\frac{c}{\nu^2}d\nu$$