Why is absolute value of the Laplacian of a function is less than or equal to a constant times magnitude of the Hessian of a function

Question

Can someone clarify why $|\Delta u| \leq n \; |D^2 u|$ for a function $ u : \mathbb{R}^n \to \mathbb{R}$ that is twice differentiable. Thanks.

Edit: According to Evan's PDE book (appendix A, page 703), $ | D^k u | = \left( \sum_{|\alpha| = k} | D^{\alpha} u|^2 \right)^{1/2}$, the $|D^2 u|$ makes sense to me. I am still searching for how this inequality is derived, maybe something with Jensen's inequality. $ | \sum_i u_{x_i x_i} | \leq C \; |D^2 u|$ for some constant $C$ seems reasonable.