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## Main Question or Discussion Point

If f and g are continuous functions on the right half-line, [0,∞], then f✶g, the convolution of f and g, is defined by

f✶g(x) = ∫

I would like to know if f✶g is a differentiable function of x.

If, for example, g(t) = 1 for t ≥ 0 then f✶g(x) = ∫

f✶g(x) = ∫

_{[0,x]}f(t)g(x-t)dt.I would like to know if f✶g is a differentiable function of x.

If, for example, g(t) = 1 for t ≥ 0 then f✶g(x) = ∫

_{[0,x]}f(t)dt has a derivative equal to f(x). But what about in general?