Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A61: 82

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

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