Chapter 3: Derivatives - Section 3.6 - The Chain Rule - Exercises 3.6 - Page 149: 42

$\frac{dy}{dt}$ = $(2\pi)sec^{2}[\pi(t)]$$tan[\pi(t)]$

$y$ = $sec^{2}[\pi(t)]$ $\frac{dy}{dt}$ = $\frac{d}{dt}$ [$sec^{2}[\pi(t)]$] $\frac{dy}{dt}$ = $(2)sec[\pi(t)]$] $\frac{d}{dt}$[$sec[\pi(t)]$] $\frac{dy}{dt}$ = $(2)sec[\pi(t)]$] [$sec[\pi(t)]tan[\pi(t)]$ $\frac{d}{dt}$$[\pi(t)]$ $\frac{dy}{dt}$ = $(2)sec[\pi(t)]$] [$sec[\pi(t)]tan[\pi(t)]$ $(\pi)$ $\frac{dy}{dt}$ = $(2\pi)sec^{2}[\pi(t)]$$tan[\pi(t)]$