Revisiting Phasors: Understanding the w in VL

[CoolDude420]

Homework Statement

Hi,

I'm revisiting phasors again. This is one of the topics I've always struggled with. Every time I do a new module, they change a lot of the convention. I've been using Schaums outline of electric circuits recently to get refreshed. I'm just confused on this one part:

Homework Equations

The Attempt at a Solution

My question is with the w that appears in the formula for VL. I understand that the current was differentiated to -sin and I understand that L is the inductance from the inductor voltage equation and that I is the amplitude from the current, but where is the w(omega, frequency) coming from at the front?

 

[blue_leaf77]

but where is the w(omega, frequency) coming from at the front?

Do you know what the first derivative is of $\cos(ax)$ with respect to $x$ with $a$ being a constant?

 

[CoolDude420]

Do you know what the first derivative is of $\cos(ax)$ with respect to $x$ with $a$ being a constant?

-asin(ax). I see now. Quite stupid of me. Guess I just got confused when we're using actual AC signals and not x. Cheers