Let $\displaystyle P[x]$ be the polynomials on the field $\displaystyle P$, and let $\displaystyle D[f(x)]=f'(x)$ be the differentiating operator. Find all the invariant subspace of $\displaystyle D$.

I think the answer is $\displaystyle P_n(x)$, the polynomial with degree less than or equal to $\displaystyle n$. But I could not prove. Would you help me?