Question: ReSubstitution of already stated expressions

Hi Guys, can someone explain how to resubstitute equations I already stated, into my final form (e.g. a derivative)?

I'm unable to substitute my g(x) expression (eq. (2)) into my derivative of f(x) (eq. (4). It only works if I state explicitly which variables to substitute via algsubs (last statement). However, for that I have to rename g(x)-->h(x). Can someone explain what I'm doing wrong here? I'd love to be able to tell maple just to use already given equations (that is g(x), eq. (2)) to simplify my derivative.

Thanks guys!

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