Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.8 Implicit Differentiation - Exercises - Page 152: 20


$$t '(x)= \frac{t \cos (x t)}{1-x \cos (x t)} $$

Work Step by Step

Given $$\sin (x t)=t$$ Differentiate with respect to $x$ \begin{align*} \frac{d}{dx} \sin (x t)&=\frac{d}{dx} t \\ \left( xt'(x)+t \right ) \cos (x t)&= t'(x) \\ \left (1-x\cos (x t) \right) t'(x)& =-t \cos (x t) \end{align*} Then $$t '(x)= \frac{t \cos (x t)}{1-x \cos (x t)} $$
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.