I'm going through a set of online lectures in Quantum Mechanics.
$Q$ is a linear operator with no explicit dependence on time $t$. $\Psi(x,t)$ is the wave function, where $x$ is a space coordinate. The professor is trying to calculate $\frac{\mathrm{d} \left \langle Q \right \rangle _\Psi }{\mathrm{d} t}$, where $\left \langle Q \right \rangle _\Psi$ is the expectation value of $Q$ in the state $\Psi$. I'm not sure if he's assuming the definition of the inner product on this particular vector space, but is $\left \langle Q \right \rangle _\Psi = \langle \Psi,Q\Psi \rangle$ a function of both $x$ and $t$? I think $x$ and $t$ are independent variables since the wave is delocalized in space, right?