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 7.2 - Natural Logarithms - Exercises 7.2 - Page 381: 36


$\frac{\ln\sqrt[3]{x}}{3\sqrt[3] {x^{2}}}-\frac{\ln\sqrt{x}}{2\sqrt x}$

Work Step by Step

$\frac{dy}{dx}$ = $\ln\sqrt[3]{x}\frac{d}{dx}(\sqrt[3] x) - \ln\sqrt{x}\frac{d}{dx}(\sqrt x)$ $\frac{dy}{dx}$ = $\ln\sqrt[3]{x}(\frac{1}{3\sqrt[3] {x^{2}}}) - \ln\sqrt{x}(\frac{1}{2\sqrt x})$ $\frac{dy}{dx}$ = $\frac{\ln\sqrt[3]{x}}{3\sqrt[3] {x^{2}}}-\frac{\ln\sqrt{x}}{2\sqrt x}$
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