Answer
$$\frac{dy}{dx}=\pi\sec^2({\pi x})$$
Work Step by Step
$$y=\tan\pi x$$ $$\frac{dy}{dx}=\frac{d(\tan\pi x)}{dx}$$
Let $u=\pi x$ and $y=\tan u$. Then, according to Chain Rule, $$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}$$ $$\frac{dy}{dx}=\frac{d(\tan u)}{du}\frac{d(\pi x)}{dx}$$ $$\frac{dy}{dx}=\sec^2 u\times\pi$$ $$\frac{dy}{dx}=\pi\sec^2({\pi x})$$
