Currently, I'm watching Sakurai's QM textbook, and I have a question on the following step :
$\int dx' |x'\rangle\langle x'-\Delta x'|\alpha\rangle=\int dx' |x'\rangle \left( \langle x'|\alpha\rangle -\Delta x' \frac{\partial}{\partial x'} \langle x'|\alpha\rangle \right)$
What happened when that $\Delta x'$ changed to $\frac{\partial}{\partial x'} \langle x'|$ ?
