I have a code that will output an expression in form of a functions like this
(Λ[θ]^3 Ω[θ] - 4 (3 Derivative[Λ][θ] Derivative[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 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[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?