Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Preliminary Questions - Page 114: 3


a) $ f(x) = x^2 $ c) $ f(x) = x ^\pi$ f) $ f(x) = x^\frac{-4}{5} $

Work Step by Step

The power rule applies only when a variable is raised to a constant power. We rule b) $ f(x) = 2\pi$ and d) $f(x) = \pi^x$ out because the value being raised is a constant. We rule e) $f(x) = x^x $ out because the variable is not being raised to a constant power.
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