Hi everyone, is the following statement true, if so, why is it true?

dE[f(x)]/dx=E[df(x)/dx]?

Thanks

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After some thought, I come up with a "heuristic" proof as the following, any idea for a rigorous proof?

dE[f(x)]/dx={E[f(x+dx)]-E[f(x)]}/dx={E[f(x)+dx*df(x)/dx]-E[f(x)]}/dx={E[f(x)]+E[dx*df(x)/dx]-E[f(x)]}/dx=dx*E[df(x)/dx]/dx=E[df(x)/dx]