Given that $f_j, g_j$ and $f,g$ are locally integrable functions, i.e. they are in $L_{loc}^1(\mathbb{R})$.
Under the assumption that $f'_j(x)=g_j(x)$ in the sense of distributions, I wanna show that $f'(x)=g(x)$ in $\mathbb{R}$ in the sense of distributions.
Any hints?
Thanks in advance.