Derivation after substitution not working

Question

I have a code that will output an expression in form of a functions like this

(Λ[θ]^3 Ω[θ] - 4 (3 Derivative[1][Λ][θ] Derivative[1][Ω][θ] + Ω[θ] ( Λ′′)[θ]) - 
 4 Λ[θ] (Ω[θ] + 3 (Ω′′)[θ]))/(4 G J Λ[θ] Ω[θ]^3)

Now, I have functions $\Lambda(\theta)$ and $\Omega(\theta)$, that I'd like to replace with some values of theta. I tried with -> and :> and none of the replacement rules will differentiate my replacement. I can differentiate the variables separately, and then specify replacement rule Λ'[θ] -> value(θ), and then use /. Derivative[1][Λ][θ]-> value[θ], but that seems kinda redundant.

Why isn't Mathematica doing it on it's own, recognising that it is the same expression, and just evaluating the derivative? This way Mathematica is treating differentiated lambdas or omegas as something not connected to original lambda and omega.

Why is this so, and can it be circumvented?

Answer 1

I hope I understood correctly what you try to do... Assume the following simple example where you have derivatives

expr=Expand[(D[f[x],{x,2}]+f[x])^3]
(* f[x]^3+3 f[x]^2 f''[x]+3 f[x] f''[x]^2+f''[x]^3 *)

The problem you are facing is that you want to apply a rule like

f[x_] :> Cos[x]*Sin[x]

This will not work on the derivatives because there FullForm does not match the lhs of the rule. What you probably want is to

1. replace the head f with your function
2. replace all x with the value

Therefore, if you know your function f[x] is now Cos[x]*Sin[x] you can do

expr /. f -> (Sin[#]*Cos[#] &)

(* -27 Cos[x]^3 Sin[x]^3 *)

and then you replace the value for x

% /. x->Pi
(* 0 *)