Question: Conditions on general functions

I am fairly new to Maple and cannot figure this out.

I'm having some trouble in computing formally the derivatives of
some composite functions

h:= x -> f(g(x)),

imposing conditions on the unknown functions f and g.

For example, I cannot find a way to impose g'(0)=0,
such that the computation of

h'(0)

simply gives 0.

 

Thank you in advance!

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