The textbook computes the time derivative of an expectation value as follows: $$\frac{d}{dt}\langle Q\rangle=\frac{d}{dt}\langle \Psi|\hat Q\Psi\rangle=\langle \frac{\partial\Psi}{\partial t}|\hat Q\Psi\rangle+\langle\Psi|\frac{\partial\hat Q}{\partial t}\Psi\rangle+\langle\Psi|\hat Q\frac{\partial\Psi}{\partial t}\rangle$$ I can't see how this could be done. The text seems to treat $\hat Q\Psi$ as a multiplication of two functions of $t$ and use the product rule of differentiation to get the result. But $\hat Q$ is a functional, its parameter is an element from the Hilbert space, not time. And $\hat Q\Psi$ means $\hat Q(\Psi)$, not $\hat Q$ times $\Psi$. So isn't $\frac{\partial\hat Q}{\partial t}$ a meaningless expression?

I guess the chain rule should be used, but the result should be the product of two derivatives instead of the sum.