/diy/ - Do It Yourself

I tried to derive some basic AC reactive formulas. Does that look right (see pic)?
I am not sure about the expression for I.
I=CdV/dt now plug in V in the Euler form and get I = C d/dt (Vo e^jwt). After taking the derivative,
I=VojwC x e^jwt. How do I show that the I leads V from here? I would want to show that
I=VowC x e^(jwt+90) . So you can get the phasor form from that. But what the heck is the physical meaning of jw in VojwC x e^jwt? That notation throws me off. The result of taking the derivative looks like a mix of a linear and phasor(euler) form.
Take a look at the pic where I typed them nicely. How do I get 6 from 4?