How to Derive Capacitive- and Inductive Reactance Formula
The phasor approach is the easiest imo. You simply let V and I become a phasor. Then you replace all of the differential operators by algebraic expressions.
Ive done the capacitor for you
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Note: in this form do not forget that both I and V are now phasors and V/I is a complex number ofcourse. 

Edit: you can notice i made the phase phi = 0. I did this to make things clear, but its value makes no difference. When you take dV/dt the phase phi is never part of that expression anyways...