Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 391: 59

Answer

$$\frac{{dy}}{{dx}} = \pi {x^{\pi - 1}}$$

Work Step by Step

$$\eqalign{ & y = {x^\pi } \cr & {\text{Find the derivative of }}y{\text{ with respect to }}x \cr & \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{x^\pi }} \right] \cr & {\text{Use the power rule for differentiation }}\frac{d}{{dx}}\left[ {{x^n}} \right] = n{x^{n - 1}};{\text{ Let }}n = \pi .{\text{ Then}}{\text{,}} \cr & \frac{{dy}}{{dx}} = \pi {x^{\pi - 1}} \cr} $$
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