Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 13 - The Trigonometric Functions - Chapter Review - Review Exercises - Page 701: 6



Work Step by Step

$$\eqalign{ & {\text{calculate }}{D_x}\tan \left( {{x^2}} \right) \cr & {\text{use the chain rule for }}{D_x}\tan x = {\sec ^2}x,{\text{ then }}{D_x}\tan u = {\sec ^2}u \cdot {D_x}u \cr & then \cr & {\text{ }}{D_x}\tan \left( {{x^2}} \right) = {\text{ se}}{{\text{c}}^2}\left( {{x^2}} \right) \cdot {D_x}\left( {{x^2}} \right) \cr & {\text{ }}{D_x}\tan \left( {{x^2}} \right) = {\text{ se}}{{\text{c}}^2}\left( {{x^2}} \right)\left( {2x} \right) \cr & {\text{ }}{D_x}\tan \left( {{x^2}} \right) = 2x{\text{ se}}{{\text{c}}^2}\left( {{x^2}} \right) \cr & {\text{therefore}}{\text{, the satement }}{D_x}\tan \left( {{x^2}} \right) = {\text{ se}}{{\text{c}}^2}\left( {{x^2}} \right){\text{ is false}} \cr} $$
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