\frac{\partial}{\partial t}(\psi,\psi)=(\frac{\partial}{\partial t}\psi,\psi)+(\psi,\frac{\partial}{\partial t}\psi)=(\frac{1}{i\hbar}\hat{H}\psi,\psi)+(\psi,\frac{1}{i\hbar}\hat{H}\psi)=-\frac{1}{i\hbar}(\hat{H}\psi,\psi)+\frac{1}{i\hbar}(\psi,\hat{H}\psi)