[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Find the derivative with respect to [math]x[/math] of each of the following functions.

• [a [math]\ln x^2[/math]
• [math]\ln(7x + 2)[/math]
• [math]\ln \sqrt{(x-3)(x+4)}[/math]
• [math]\ln(x^2 - 9x + 3)[/math]
• [math]\ln frac2x[/math]
• [math]\ln \sqrt[7]{7x^3}[/math]
• [math]\int_1^{x^2+3} \frac{dt}t[/math]
• [math](\ln x)^3[/math]
• [math]\ln(\ln x)[/math]
• [math]\ln x\sqrt{x-1}[/math]
• [math]\ln \frac{x-3}{x+1}[/math]
• [math]\ln \frac{x^2-2x+4}{x^2+1}[/math]
• [math]\ln \frac{x}{2-x^2}[/math].