University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 38



Work Step by Step

given $y=20(3x-4)^\frac{1}{4}{(3x-4)^\frac{-1}{5}}$ $y=20{(3x-4)^{(\frac{1}{4}-\frac{1}{5}})}=20{(3x-4)^{(\frac{1}{20})}}$ on differentiating both sides: $\frac{dy}{dx}=\frac{d{(20{(3x-4)^{(\frac{1}{20})}}})}{dx}$ $\frac{dy}{dx}=20\frac{1}{20}{(3x-4)^{(\frac{-19}{20})}}{\frac{d(3x-4)}{dx}}$ $\frac{dy}{dx}={3}{(3x-4)^{(\frac{-19}{20})}}$
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