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videoList.tex
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\documentclass[11pt]{article}
\usepackage{graphicx}
\usepackage{amssymb}
\begin{document}
\section{Week 4}
\subsection{3.2}
\begin{itemize}
\item Use given graph to estimate derivative
\item Find graph of $f'$ based on graph of $f$.
\item mooc - $f(x) = \vert x \vert$ not differentiable at $x = 0$
\item $f(x) = x^2 + 2, x \geq 3; 6x-7, x < 3$ differentiable at 3?
\end{itemize}
\subsection{3.3}
\begin{itemize}
\item $\frac{d}{dx} c = 0$, $\frac{d}{dx} (x) = 1$
\item $\frac{d}{dx} x^4 = 4x^3$, $\frac{d}{dx} x^n = nx^{n-1}$
\item mooc: constant multiple of $f(x)$, derivative of derivative
\item $f(x) + g(x)$ derivative
\item $f(x) = 3x^4 - 9x + 7$ derivative
\item derivative of $a^x$
\item written ex. up to $f^{(4)}(x)$ for $f(x) = 3x^4 + 2x^3 + 7x + 5e^x$
\end{itemize}
\section*{Week 5}
\subsection{Product and Quotient Rules}
\begin{itemize}
\item half marathon stride 2.7 feet, 180 strides/min. Increase to 3ft/stride, cadence to 190
\item $f'(x)$ for $f(x) = x^3e^x$
\item $\frac{x^2 + 5x - 3}{2x^2 + 7}$, $e^{-x}$, $x^{-3}$, $\frac{x^4e^x}{7x^2 -1 }$
\item $e^{2x}$ as $e^x e^x$, also $e^{3x}$
\item Gnats in your kitchen
\end{itemize}
\subsection{Derivatives of Trig Functions}
\begin{itemize}
\item $\lim_{x\to0} \frac{\sin(x)}{x}$, $\lim_{x\to 0} \frac{\cos(x) - 1}{x}$
\item $\lim_{x \to 0} \frac{\sin(5x)}{x}$, $\lim_{x \to 0} \frac{\sin(5x)}{7x}$, $\lim_{x \to 0} \frac{\sin(x-2)}{x^2 - 4}$
\item derivatives $e^{3x}\cos(x)$, $4\sin(x) - x\cos(x)$, $\frac{1+\cos(x)}{1-\cos(x)}$, 2nd derivative $\csc(x)$
\end{itemize}
\subsection{Derivatives as rates of change}
\begin{itemize}
\item slides: velocity of a golf ball $s(t) = 15t - 1.86t^2$ after 1 second
\item slides: rumor $p(t) = \frac{1}{1+ae^{-kt}}$
\item slides: bacteria $p(t) = \frac{1000}{1+6e^{-0.7t}}$
\item slides: moles/liter $C(t) = \frac{45t}{9t+1}$
\item Instantaneous velocity given graph, greatest inst. velocity? speed greatest? stopped? Given: $s(t) = t^3 - 6t^2 + 9t$, find $v(t)$, $v(1)$, $a(t)$, $a(1)$.
\item cell phone users $f(t) = 30t^2 + 70.8t - 45.8$ 1998 - 2013, inst. growth rate in 2009
\item DVD players $C(x) = 5000 + 5x + 0.01x^2$. find average cost of 500 dvds, cost of 501st?
\end{itemize}
\section*{Week 6}
\subsection{3.7: The Chain Rule}
\begin{itemize}
\item Truck driver earns \$5 per mile, average speed 42 mph: composition example
\item $F(x) = \sqrt{x^2 +1}$
\item $y(x) = \tan(12x^2 - 2)$
\item $\sin(x^2)$ vs $\sin^2(x)$
\item Mooculus Week 5 - lecture 1
\item $y = (1 + 2x)^5$, $e^{\tan x}$, $\sin(x^5 + 5x^2 + 8)$, $\cos (e^{7x^2})$
\item $f(x) = -9e^{x \sin x}$
\item $f(x) = \frac{\sin(5x)}{e^{\tan x} + 17x}$ (error in video)
\item $e^{x^2 + 1}\sin(x^3)$, $\left ( \frac{3x}{4x+2} \right ) ^5$, $\frac{xe^x}{x+1}$
\item Find equation of tangent line to $y = e^{3x}$ at $x = \frac13\ln 3$
\end{itemize}
\subsection{3.8: Implicit Differentiation}
\begin{itemize}
\item $x^4$, $y^4$, $(f(x))^4$ WRT $x$, $x^4$, $y^4$ WRT $y$
\item mooculus Week 5 - lecture 3
\item Find $y'$ for $x^3 + y^3 = 6xy$
\item $x^{2/3}$ derivative
\item $x^3 +y^3 - 9xy = 0$, $\sin(xy) = 7y+2$, $x^4 - x^2y + y^4 = 1$ (horizontal tangent lines) $x^2 + y^2 = 9$ (2nd derivative) $x^{21/17}$, $2x^2 + xy - 3y^3 = 8$ equation of tangent line at $(2,1)$
\end{itemize}
\subsection{3.9: derivatives of Logs and Exponential Functions}
\begin{itemize}
\item $f(x) = \ln(x)$
\item $f(x) = a^x$
\item $f(x) = \log_a(x)$
\item $\ln(3x)$, $3^{5x}$, $\log_7(5x+2)$
\item Mooculus, Week 5 - lecture 7, lecture 9
\item $f(x) = \frac{(2x+7)^4 \sqrt{5x-1}}{(x^3 + 7x)^{2/3}}$
\item $f(x) = \frac{\cos^8(x)}{(11x+2)^6}$
\item $2^{\sin(x)}$, $5 \cdot 3^{2x^2 + 7x+3}$
\item $f(x) = x^x$, $(\sin(x)^{\cos(x)}$, $x^{\ln x} + 8x^2$
\end{itemize}
\section*{Week 7}
\subsection{3.10: Derivatives of Inverse Trig Functions}
\begin{itemize}
\item mooc week 6 - lecture 7, 8
\item mooc week 5 - lecture 5
\item Inverse functions review $f(x) = (x-5)^2 + 3$
\item review gallery
\item derivatives of arcsin, arccos
\item $\frac{d}{dx} (\sqrt{x})$, $\frac{d}{dx} \arctan(x)$, $\frac{d}{dx} \ln(x)$ via inverse functions
\item $f(x) = 5x^2 + x$ equation of tangent line of $f^{-1}(y)$ when x = 1
\item $\frac{d}{dx} \cos(\sin^{-1} 4x)$, $\frac{d}{dx} x \cot^{-1}(x/9)$.
\end{itemize}
\subsection{3.11: Related Rates}
\begin{itemize}
\item 6ft tall man, 9ft/sec towards 20 ft street light. rate of shadow when 18ft from light.
\item 25 ft ladder, slides down at 1ft/sec. How fast when bottom is 7ft away?
\item slides: spherical balloon 20 cu ft per min, how fast is $r$ increasing when (a) $r = 1$ft (b) $r= 2$ft
\item convict walks 6ft/sec, searchlight 30 ft from path, what rate of rotation when man is 40ft from light
\item trough 12 ft long, 4ft across top. Ends isosceles triangles, altitude 3ft. water in 2 cu ft per min. How fast water rising when 1ft deep?
\item mooc, week 7 lecture 6, 9
\item sand dumped from truck at 17 cu ft per min, conical pile diameter twice height. how fast height increasing when base is 6ft around?
\end{itemize}
\end{document}