Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 151: 29

$H'(\theta)=\sin \theta+\theta \cos \theta$ $H''(\theta)= 2\cos \theta-\theta \sin \theta$

$H'(\theta)= \frac{d}{d\theta}(\theta\sin \theta)= 1\times\sin \theta+\theta\times\cos\theta$ $=\sin \theta+\theta \cos \theta$ $H''(\theta)=\frac{d}{d\theta}(\sin\theta)+\frac{d}{d\theta}(\theta\cos\theta)$ $\cos \theta+ 1\times\cos \theta+ \theta\times-\sin\theta$ $=2\cos \theta-\theta \sin \theta$