Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 18


$$ f'(x) =\frac{\sin x-x\cos x+2}{(\sin x+2)^2} .$$

Work Step by Step

Since $ f(x)= \frac{x}{\sin x+2}$, then using the quotient rule, the derivative is giving by $$ f'(x)=\frac{(\sin x+2)(1)-x(\cos x)}{(\sin x+2)^2} \\ =\frac{\sin x-x\cos x+2}{(\sin x+2)^2} .$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.