Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 28



Work Step by Step

Using the product rule, we obtain $f'(x)=$$\frac{d}{dx}(x^{3/2})\times(2x^{4}-3x+x^{-1/2})+x^{3/2}\times\frac{d}{dx}(2x^{4}-3x+x^{-1/2})$ $=(\frac{3}{2}x^{1/2})(2x^{4}-3x+x^{-1/2})+x^{3/2}\times(8x^{3}-3-\frac{1}{2}x^{-3/2})$ $=3x^{9/2}-\frac{9}{2}x^{3/2}+\frac{3}{2}+8x^{9/2}-3x^{3/2}-\frac{1}{2}$ $=11x^{9/2}-\frac{15}{2}x^{3/2}+1$
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