Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.7 Derivatives And Integrals Involving Inverse Trigonometric Functions - Exercises Set 6.7: 54

Answer

True.

Work Step by Step

The derivative of a function $f(x) = sin^{-1}(x)+cos^{-1}(x)$ is simply $$f'(x)=\frac{1}{\sqrt{1+x^{2}}}-\frac{1}{\sqrt{1+x^{2}}}=0$$ If the derivative of a function is zero for all values, the function must be constant. For proof, integrating zero yields a constant.
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