# Differentiation of the norm

Let $f = f(t,x) = f(t, x_1, \cdots , x_n) .$ If $f \in C^1 ([0,M],W^{s,2}(\Bbb R^n))$ (which means that $g(t) :=\| f \|_{W^{s,2}(\Bbb R^n)}$ is differentiable on $[0,M]$ and $\frac{d}{dt} g(t)$ is continuous on $[0,M]$), then can I conclude that $h(t) := \| \partial_t f \|_{W^{s,2}(\Bbb R^n)}$ is also continuous on $[0,M]$?
Here $W^{s,2}$ means the general Sobolev space, and let $s$ be an integer.

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