Answer
$ 1+t^{-2}$
Work Step by Step
Use derivative formula; $f(x)= x^n \implies f'(x)= n x^{n-1}$
Consider $v(t) = t - \dfrac{1}{t}=t-t^{-1}$
Now, $v'(t) = (1)t^{(1-1)}-(-1)t^{(-1-1)}= 1+t^{-2}$
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 3.2 - The Derivative as a Function - Exercises 3.2 - Page 115: 10
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