Chapter 12 - Section 12.3 - Higher Order Derivatives: Acceleration and Concavity - Exercises - Page 901: 10

$\displaystyle \frac{6}{x^{4}}-\frac{1}{x^{2}}$

$f''(x)=\displaystyle \frac{d}{dx}\left[\frac{df}{dx}\right]=\frac{d^{2}f}{dx^{2}}$ $\displaystyle \frac{dy}{dx}=\frac{d}{dx}[x^{-2}+\ln x]=-2x^{-3}+\frac{1}{x}$ $\displaystyle \frac{d^{2}y}{dx^{2}}=\frac{d}{dx}[ -2x^{-3}+x^{-1}]=-2(-3x^{-4})+(-x^{-2})= \displaystyle \frac{6}{x^{4}}-\frac{1}{x^{2}}$