An inequality for the $W^{k,1}(\mathbb{R}^n)$

Question

Let $k\in\mathbb{N}$ and $Q=(0,1)^n$, $u\in W^{k,1}_{loc}(\mathbb{R}^n)$ do we have an inequality $\sum\limits_{|a|\leq k}\|\frac{\partial ^a}{\partial x^a}w\|_{L^1(Q)}\leq C\|w\|_{L^1(Q)}+C\sum\limits_{|a|=k}\|\frac{\partial ^a}{\partial x^a}w\|_{L^1(Q)}$. It is better, if we have $\sum\limits_{|a|\leq k}\|\frac{\partial ^a}{\partial x^a}w\|_{L^1(Q)}\leq C\sum\limits_{|a|=k}\|\frac{\partial ^a}{\partial x^a}w\|_{L^1(Q)}$. The first inequality somehow follows by the Sobolev embedding, but I dont know why.