Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises - Page 196: 10

$y'=\cos^{2}\theta-\sin^{2}\theta$

$y=\sin\theta\cos\theta$ Differentiate using the product rule: $y'=(\sin\theta)(\cos\theta)'+(\cos\theta)(\sin\theta)'=...$ $...=(\sin\theta)(-\sin\theta)+(\cos\theta)(cos\theta)=-\sin^{2}\theta+\cos^{2}\theta=\cos^{2}\theta-\sin^{2}\theta$