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: 33


$$ f'(x)= \frac{(x+1)(\frac{7}{2}x^{5/2}+\frac{3}{2}x^{1/2})-(x^{7/2}+x^{3/2})}{(x+1)^2}.$$

Work Step by Step

We rewrite $ f(x)$ as follows $$ f(x)=\frac{x^{3/2}(x^2+1)}{x+1}=\frac{x^{7/2}+x^{3/2}}{x+1}.$$ Now, the derivative $ f'(x)$, using the quotient rule, is given by $$ f'(x)= \frac{(x+1)(\frac{7}{2}x^{5/2}+\frac{3}{2}x^{1/2})-(x^{7/2}+x^{3/2})}{(x+1)^2}.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.