How to find this derivative?

Question

If $p = \frac{hv}{c}$ then how is $p^2 dp = \frac{h^3v^2}{c^3}dv$? What I arrived at is $\frac{2 h^2 v}{c^2}dv$.

Answer 1

Just note that $p=\frac{hv}{c}$ implies that $dp = \frac hc dv$ and so $$ p^2 dp = \left( \frac{hv}{c}\right)^2 \frac hc dv = \frac{h^3 v^2}{c^3} dv $$

Answer 2

If the answer is $\frac{h^3v^2}{c^3}dv$,

I guess this is nothing about derivatives, it's just multiplication

Let $p^2=\frac{h^2v^2}{c^2}$ and $dp=\frac{hdv}{c}$, Then $$p^2dp=dp^3=\frac{h^3dv^3}{c^3}=\frac{h^3v^2}{c^3}dv$$