Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises - Page 196: 5

$y'=\sec^{3}\theta+\sec\theta\tan^{2}\theta$

$y=\sec\theta\tan\theta$ Differentiate using the product rule: $y'=(\sec\theta)(\tan\theta)'+(\tan\theta)(\sec\theta)'=...$ $...=(\sec\theta)(\sec^{2}\theta)+(\tan\theta)(\sec\theta\tan\theta)=...$ $...=\sec^{3}\theta+\sec\theta\tan^{2}\theta$