Basic calculation problem with commutators

[Unkraut]

Homework Statement

A is a Hermitian operator which commutes with the Hamiltonian: $\left[A,H\right]=AH-HA=0$

To be shown: $\frac{d}{dt}A=0$

Homework Equations

Schrödinger equation: $i\hbar\frac{\partial}{\partial t}\psi=H\psi$ with the Hamilton operator H.

The Attempt at a Solution

I have seen this solution on many sites:

$\frac{d}{dt}<A>=\frac{d}{dt}<\psi|A|\psi>=<\psi|\frac{\partial A}{\partial t}|\psi>+<\frac{d\psi}{dt}|A|\psi>+<\psi|A|\frac{d\psi}{dt}>=<\frac{\partial A}{\partial t}>+\frac{1}{i\hbar}<\left[ A, H\right] >=0$

I have a problem with this: $<\frac{d\psi}{dt}|A|\psi>+<\psi|A|\frac{d\psi}{dt}>=\frac{1}{i\hbar}<\left[ A, H\right] >$

Okay, obviously we have from the Schrödinger equation:
$H=i\hbar\frac{\partial}{\partial t}$
and thus
$\frac{\partial}{\partial t}=\frac{1}{i\hbar}H$
and thus
$<\frac{d\psi}{dt}|A|\psi>+<\psi|A|\frac{d\psi}{dt}>=\frac{1}{i\hbar}(<H\psi|A|\psi>+<\psi|A|H\psi>)=\frac{1}{i\hbar}<\psi|HA+AH|\psi>$

But this is not the commutator but the anti-commutator. It is plus and not minus! What did I do wrong here?

 

[Dick]

Remember <a|ib>=i*<a|b> but <ia|b>=(-i)*<a|b>.

 

[Unkraut]

Oh, of course!
Thank you.