Answer
$y'=-\frac{1}{\sqrt{(1-(sin^{-1}t)^2)(1-t^2)}}$
Work Step by Step
$y=cos^{-1}(sin^{-1}t)\\
y'=-\frac{1}{\sqrt{1-(sin^{-1}t)^2}}\times{\frac{1}{\sqrt{1-t^2}}}\\
y'=-\frac{1}{\sqrt{(1-(sin^{-1}t)^2)(1-t^2)}}$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 3 - Section 3.5 - Implicit Differentiation - 3.5 Exercises - Page 216: 58
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