$$⟨\psi \left|𝒯\left\{\frac{\delta }{\delta \varphi }F\left[\varphi \right]\right\}\right|\psi ⟩=-i⟨\psi |𝒯\left\{F\left[\varphi \right]\frac{\delta }{\delta \varphi }S\left[\varphi \right]\}\right|\psi ⟩$$