Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 163: 39


$$ y'=2x -\frac{3}{2}x^{-5/2} .$$

Work Step by Step

Since $ y=\frac{x^4+\sqrt x}{x^2}$, we simplify $ y $ as follows $$ y=\frac{x^4+\sqrt x}{x^2}= x^2+\frac{\sqrt x}{x^2} =x^2+x^{-3/2}.$$ Recall that $(x^n)'=nx^{n-1}$ Now, the derivative $ y'$ is given by $$ y'=2x -\frac{3}{2}x^{-5/2} .$$
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