Proof that current is the rate of change of charge with respect to time

I've been looking for a proof of this but its impossible to find one.
Ive started with the fact that E=QV
therefore dQ/dt=d(E/V)/dt
dE/dt= power = P= IV
but I'm stuck with derivative of voltage.
I know quotient rule will help.

thanks

Instead of using calculus, you could just use normal equations:
$E=QV$ and $\frac{E}{t}=P=IV$
Equate the two equations for E:

$\frac{E}{t}=\frac{QV}{t}=P=IV$

Cancel the voltages off both sides after combining:
$\frac{QV}{t}=IV \rightarrow \frac{Q}{t}=I$

So current is change in charge, respect to time.