# Lesson Series

A list of figures for Calculus in 5 Hours

In this lesson we review what a functions is, important terms related to them, and provide you with a tool to graph them.

In this lesson we review the concept of a straight line and its two main features - slope and y-intercept. We discuss polynomials and provide interactive tools to graph straight lines and polynomials.

We discuss the different ways that functions can be combined.

We briefly describe differential calculus and integral calculus. We provide pictures and basic notation of both.

Here we cover the four most important derivatives that you will need.

The Tangent Line is a straight line at a specific point, $x_0$, whose slope is $f\,'(x_0)$ that takes on the value $f(x_0)$ at $x_0$. In this lesson we derive the formula for the tangent line given that we know the function and its derivative.

In this lesson we tell you the derivative of a polynomial and give you a tool for calculating its derivative both symbolically and numerically at any point.

The product rule gives us a quick way of finding the derivative of the multiplication of two functions. The product rule is
\[
\frac{d}{dx}fg=g\frac{df}{dx}+f\frac{dg}{dx}.
\]

The quotient rule is a quick way to find the derivative of the division of two functions. The quotient rule states that
\[
\frac{d}{dx}\left(\frac{f}{g}\right)=\frac{1}{g^2}\left(g\frac{df}{dx}-f\frac{dg}{dx}\right).
\]

The Chain Rule shows how to find the derivative of a function composition. The Chain Rule states that \[\frac{d}{dx}\left[f\circ g\right] =\frac{df}{dg}\cdot\frac{dg}{dx}.\]