[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]

For each of the following equations calculate [math]\dydx[/math] at the point specified.

• [math]4x^2 + y^2 = 8[/math], at the point [math](1, 2)[/math].
• [math]y^2 = x[/math], at the point [math](4, 2)[/math].
• [math]y^2 = x^5[/math], at one point [math](1,1)[/math].
• [math]y^2 = \frac{x-1}{x+1}[/math], at the point [math](a,b)[/math].
• [math]y^2 = \frac{x^2-1}{x^2+1}[/math], at the point [math](a,b)[/math].
• [math]x^2y + xy^2 = 6[/math], at the point [math](1,2)[/math].
• [math]x^2 + 2xy = 3y^2[/math], at the point [math](1,1)[/math].
• [math]5y^2 = x^2y + \frac{2}{xy^2}[/math], at the point [math](2,1)[/math].
• [math]x^\frac32 + y^\frac32 = 2[/math], at the point [math](1,1)[/math].
• [math]x^5 + 3x^2y^3 + 3x^3y^2 + y^5 = 8[/math], at the point [math](1,1)[/math].