## University Calculus: Early Transcendentals (3rd Edition)

$$\frac{dy}{dt}==2\pi\sec^2\pi t\tan\pi t$$
According to the Chain Rule: $$\frac{dy}{dt}=\frac{d}{dt}(\sec^2\pi t)$$ $$\frac{dy}{dt}=2\sec\pi t\frac{d}{dt}(\sec \pi t)$$ $$\frac{dy}{dt}=2\sec\pi t(\sec\pi t\tan\pi t)\frac{d}{dt}(\pi t)$$ $$\frac{dy}{dt}=2\sec^2\pi t\tan\pi t\times(\pi)=2\pi\sec^2\pi t\tan\pi t$$