# Differentiating nested functions, Differentiate unevaluated function

I have two functions

    G[x_]:=x^6;
S[x_]:=G[x]+x^12


I would like to operate on S[x] with respect to x in three ways, where we take the differentiation as an example for an operator

1. Plug in G[x] in S[x] and then differentiate

2. Do not plug in G[x] in S[x] and differentiate, such that x^12 is evaluated, but G[x] is only evaluated symbolically to G'[x]

3. Do not plug in G[x] in S[x] and regard G[x] as a constant.

While 1. has an obvious solution, do you have an idea how to realize 2. and 3. without changing the lines of code given above, in particular without re-defining G every time?

I tried to build an operator consisting of different elements such as Unevaluated, Defer, Inactivate, Hold and Replace, but either G[x] gets plugged into S[x] or the differentiation is incorrect.

Can I give the function G[x] (temporarily) the Attribute "Constant" for 3.?

Best regards

Maybe you can use Block and Inactive:

S'[x]
Block[{G = Inactive[G]}, S'[x]]
Block[{G},
G /: Derivative[G] = 0&; (* G is a constant *)
With[{r = S'[x]},
Inactivate[r, G]
]
]


6 x^5 + 12 x^11

12 x^11 + Inactive[G]'[x]

12 x^11

Here are some ways to approach this. For 1:

s[x_] := g[x] + x^12;
g[x_] = x^6;
D[s[x], x]
6 x^5 + 12 x^11


For 2:

Clear[g]
D[s[x], x]
12 x^11 + g'[x]


For 3:

g[x_] = c;
D[s[x], x]
12 x^11

• Thank you for your attempt, but it is important not to change G[x_] every time. – Uwe.Schneider Aug 24 '18 at 16:39