Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5: 24

Answer

The Derivative is: $\frac{dr}{d\theta}=\theta\cos\theta$

Work Step by Step

$r=\theta\sin\theta+\cos\theta$ Applying Derivative rules: $y'=f'(x)+g'(x)$ $and$ $f'(x)=h'(x)\cdot v(x)+h(x)\cdot v'(x)$ $\frac{dr}{d\theta}=\frac{d}{d\theta}(\theta\sin\theta)+\frac{d}{d\theta}(\cos\theta)$ $\frac{dr}{d\theta}=(\theta^{1-1}(\sin\theta)+\theta(\cos\theta))+(-\sin\theta)$ $\frac{dr}{d\theta}=\sin\theta+\theta\cos\theta-\sin\theta$ $\frac{dr}{d\theta}=\theta\cos\theta$
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