Electrical Power Related

I am studying DC circuits and trying to derive formula for power; that is in fact
$$P = I.Vab$$

where Vab is the potential difference between two terminals of a circuit element.

From my previous studies, I know that.

$$P = dW / dt$$

I assume that for a small interval, dt, a single charge q has a small displacement , dx.

Then;

$$dW = E q dx$$

where E is magnitude of the electric field.

Hence, from the formula above,

$$P = E q dx / dt$$

This is all I could come up with. I want to go on with this idea to prove

$$P = I Vab$$

I know I need to substitute dq somewhere (to get I ) , somehow.. Simply replacing q with dq does not seem to work; it leads to an incorrect formula. (I find P = I dV ; I guess, if I do that.)

MATLABdude
$$dW = E q dx$$