How can I remove vanishing derivatives of hypergeometric functions?

I have a lot of expressions containing derivatives of hypergeometric functions of the sort:

$$_2F_1^{(0,0,1,0)} left(frac{1}{2} , 1 ; frac{3}{2} ; 0 right). tag{1}$$

The last argument is always $0$. This is not evaluated, but if I used N then it evaluates to $0$. How can such expressions consistently be removed from my expressions?

Consider the following example (sorry I do not know how to properly format the hypergeometric function in the code environment, it’s just copy-paste):

15 g^2 f[1] [CapitalDelta]c[1] - 30 g^2 f[1] [CapitalDelta]c[1] !(*SuperscriptBox[(Hypergeometric2F1), TagBox[RowBox[{"(", RowBox[{"0", ",", "0", ",", "1", ",", "0"}], ")"}], Derivative], MultilineFunction->None])[1/2, 2, 5/2, 0]

The second term evaluates to $0$ with N. I can use /.{... -> N[...]} but since I have a lot of functions it would be better to use something else.

Clear["Global`*"]

Derivative[1, 0, 0, 0][Hypergeometric2F1][1/2, 1, 3/2, 0] + 
  Derivative[0, 0, 1, 0][Hypergeometric2F1][1/2, 1, 3/2, 0] + 
  Derivative[0, 1, 0, 0][Hypergeometric2F1][1/2, 1, 3/2, 0] +
  Derivative[1, 0, 0, 0][Hypergeometric2F1][1/2, 1, 5/2, 0]  /. 
 _?(N[#] == 0 &) :> 0 

(* 0 *)