Answer
The Derivative is:
$\frac{ds}{dt}=\sec^2 t-1$
Work Step by Step
$s=\tan t - t$
Applying derivative rules:
$\frac{ds}{dt}=\frac{d}{dt}(\tan t)-\frac{d}{dt}(t)$
$\frac{ds}{dt}=(sec^2 t) -((1)t^{1-1})$
$\frac{ds}{dt}=\sec^2 t-1$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
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 - Page 141: 19
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