So I've been given the function:

$\displaystyle f(x)=3x^3-9x$ and I found $\displaystyle f' , f''$ and I graphed them all together but I'm trying to understand: in general what is the relationship among the degrees of a polynomial function and the degress of its successive derivatives?

Also what is the releshonship among the degrees of $\displaystyle f$ and its successive derivatives?