Hello,

this relationship is false, it's an equality when dx goes to 0.dE[f(x)]/dx={E[f(x+dx)]-E[f(x)]}/dx

And how does df/dx appear in the third member (after the second equality) ?

And... where does this relationship come from ?

Because E(f(x)) is a constant, so its derivative is 0. And E(df(x)/dx) is not necessarily 0.

Also, I think taking x instead of X, a random variable, is inconsistent, as it makes the problem "trivial" or "weird" lol