= Solution
\b[Not as ordinary convergent <Fourier series>], for a nontrivial moving ramp. Formal spatial differentiation would give
$$
\frac{2K}{L}\sum_{n=1}^\infty(-1)^{n+1}
\cos\left[\frac{2\pi n}{L}(x-vt)\right],
$$
and formal time differentiation multiplies that expression by $-v$. The summands have nondecaying amplitude and do not tend to zero, so the ordinary series cannot converge. The periodic extension has jumps, violating the regularity needed for <Termwise differentiation of a Fourier series>.
Away from the moving jumps, the classical <derivatives> exist and are $g_x=K/L$ and $g_t=-vK/L$. A <distributional derivative> also includes the <Dirac delta distribution> contributions at the jumps, so distributional differentiation is possible, but it is a different interpretation. If $v=0$, the time <derivative> is trivially zero; if $K=0$, both <derivatives> are zero.
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