$ Vmcos(\omega t+ \phi) = Acos(\omega t)+Bsin(\omega t)\, $
$ Vm = \sqrt {A^2+B^2} $ and $ \,\ \phi= \tan^{-1} \frac{-B}{A}\, $
Differentiation Property $ \,\ \frac{d}{dt}Re[A e ^{j \omega t}] = Re [\frac{d}{dt} (A e ^{j \omega t})]=Re[j \omega A e^{j \omega t}] $
