Show that $f$ is a Schwartz function if and only if $|\partial^\alpha \phi(x)| \leq C_{\alpha ,N}(1+|x|)^{-N} $

Question

Show that a smooth function $f$ is in Schwartz space if only if for all $\alpha\geq 0$ and $N\geq 0$ there is a constant $C_{\alpha,N}$ such that $$|\partial^\alpha \phi(x)| \leq C_{\alpha ,N}(1+|x|)^{-N}$$ for all $x\in\mathbb{R}^N$.