Sin(x)=eix–e−ix2i Sin(x) = \frac{e^{ix} – e^{-ix}}{2i} Sin(x)=2ieix–e−ix ddxSin(x)=ddx(eix–e−ix2i) \frac{d}{dx} Sin(x) = \frac{d}{dx} ( \frac{e^{ix} – e^-{ix}}{2i} ) dxdSin(x)=dxd(2ieix–e−ix) 12iis a constant \frac{1}{2i} is a constant 2i1is a constant 12iddx(eix–e−ix) \frac{1}{2i} \frac{d}{dx} ( e^{ix} – e^{-ix} ) 2i1dxd(eix–e−ix) 12i[ddx(eix)–ddx(e−ix)] \frac{1}{2i} [\frac{d}{dx} ( e^{ix} ) – \frac{d}{dx} (e^{-ix} ) ] 2i1[dxd(eix)–dxd(e−ix)] 12i[ieix–(−ie−ix)] \frac{1}{2i} [ i e^{ix} – ( -i e^{-ix} ) ] 2i1[ieix–(−ie−ix)] 12i[ieix+ie−ix] \frac{1}{2i} [ ie^{ix} + ie^{-ix}]2i1[ieix+ie−ix] i2i[eix+e−ix] \frac{i}{2i} [ e^{ix} + e^{-ix}]2ii[eix+e−ix] 12[eix+e−ix]=Cos(x) \frac{1}{2} [ e^{ix} + e^{-ix}] = Cos(x)21[eix+e−ix]=Cos(x)