How to find the derivative of an output in Laplace domain

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I have a $Y(s)=F(s)\cdot X(s)$. Because it is a close feedback loop, I know F(s), but didn't compute the inverse Laplace transform of it because I don't know if $y(t) = f(t) \cdot x(t)$. The input x is a "known value" but it could be a constant or a function of time. However, the problem I am solving requires me to find the Laplace transformation of the derivative of y(t). But I don't know how to proceed from here.