Thomas' Calculus 13th Edition

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

Chapter 3: Derivatives - Practice Exercises - Page 178: 34



Work Step by Step

Rewrite the equation: $y=4x(x+x^{1/2})^{1/2}$ Take the derivative of the equation using Product Rule, Power Rule, and Chain Rule: $y'=4x\times\frac{1}{2}(x+x^{1/2})^{-1/2}\times(1+\frac{1}{2}x^{-1/2})+4(x+x^{1/2})^{1/2}$ $=(2x+x^{1/2})(x+x^{1/2})^{-1/2}+4(x+x^{1/2})^{1/2}$
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