Assume that $f(x),g(x)$ are positive and are in $L^1$. Moreover, they are differentiable and their derivative is integrable. Let $h(x)=f(x)*g(x)$, the convolution of $f$ and $g$. Does the derivative of $h(x)$ exist? If yes, how can we prove that $ \frac{d}{dx}(f(x)*g(x)) = (\frac{d}{dx}f(x))*g(x)$
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