How to show that $u(t,x)\in C([0,T],H^{1}(\mathbb{R}^{n}))$?

Question

If $u(t,x)\in L^{2}([0,T],H^{2}(\mathbb{R}^{n}))$, $\partial_{t}u \in L^{2}([0,T],L^{2}(\mathbb{R}^{n}))$, prove that $$ u(t,x)\in C([0,T],H^{1}(\mathbb{R}^{n})) $$