\frac{d}{dt}\sum_{n=1}^{\infty}(an\cos{\frac{2n\pi t}{b-a}}+bn\sin{\frac{2n\pi t}{b-a}})=\frac{d}{dt}(\sum_{n=1}^{\infty}an\cos{\frac{2n\pi t}{b-a}}+\sum_{n=1}^{\infty}bn\sin{\frac{2n\pi t}{b-a}})=\sum_{n=1}^{\infty}\frac{d}{dt}(an\cos{\frac{2n\pi t}{b-a}})+\sum_{n=1}^{\infty}\frac{d}{dt}(bn\sin{\frac{2n\pi t}{b-a}})