Sin(x) = \frac{e^{ix} – e^{-ix}}{2i} \frac{d}{dx} Sin(x) = \frac{d}{dx} ( \frac{e^{ix} – e^-{ix}}{2i} ) \frac{1}{2i} is a constant \frac{1}{2i} \frac{d}{dx} ( e^{ix} – e^{-ix} ) \frac{1}{2i} [\frac{d}{dx} ( e^{ix} ) – \frac{d}{dx} (e^{-ix} ) ] \frac{1}{2i} [ i e^{ix} – ( -i e^{-ix} ) ] \frac{1}{2i} [ ie^{ix} + ie^{-ix}] \frac{i}{2i} [ e^{ix} + e^{-ix}] \frac{1}{2} [ e^{ix} + e^{-ix}] = Cos(x)