Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A61: 77

Answer

$ \frac{x(3x^2+2)}{(x^2+1)^{1/2}}$

Work Step by Step

$2x(x^2+1)^{1/2}+x^2\cdot\frac{1}{2}(x^2+1)^{-1/2}\cdot2x=2x(x^2+1)^{1/2}+\frac{x^3}{(x^2+1)^{1/2}}=\frac{2x(x^2+1)+x^3}{(x^2+1)^{1/2}}=\frac{3x^3+2x}{(x^2+1)^{1/2}}=\frac{x(3x^2+2)}{(x^2+1)^{1/2}}$
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