Answer
$\frac{10}{100x^{2}+1}$
Work Step by Step
Recall that $tan^{-1} x= \frac{1}{1+x^{2}}$
Then, using chain rule, we get
$tan^{-1}(10x)= \frac{1}{(10x)^{2}+1}\cdot\frac{d(10x)}{dx}=\frac{10}{100x^{2}+1}$
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 3 - Derivatives - 3.10 Derivatives of Inverse Trigonometric Functions - 3.10 Execises - Page 221: 13
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