exercise:Eacda3e256

[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} \renewcommand{\d}{d} [/math]

Find the following differentials.

• [math]\d(x^2 + x + 1) = \cdots[/math]
• [math]\d(7x + 2) = \cdots[/math]
• [math]\d(x^3+1)(5x-1)^3 = \cdots[/math]
• [math]\d\left( \frac{x-1}{x+1} \right) = \cdots[/math]
• [math]\d u^7 = \cdots[/math]
• [math]\d \left( \frac{u^2}{v^2} \right) = \cdots[/math]
• [math]\d(az^2 + bz + c) = \cdots[/math] ([math]a[/math], [math]b[/math], and [math]c[/math] are constants)
• [math]\d\sqrt{1 + \sqrt{1+x}} = \cdots[/math]
• [math]\d x = \cdots[/math]
• [math]\d (u^2 + 2)(v^3 - 1) = \cdots[/math]