In this lesson, we learn about derivatives and how they extend the idea of slope from algebra to curves. We are shown how to find the slope of a graph at a single point using the formal definition of a derivative, which involves finding the limit as h approaches 0 of (f(x+h)-f(x))/h. We are given a detailed example of finding a derivative using this definition, as well as a simpler method for finding the derivative of polynomial equations. Finally, we learn about the usefulness of derivatives in determining the slope of a curve at any point and how it relates to the original equation.
A quick introduction to derivatives for the student having trouble understanding the concept of a derivative. An explanation of how to find the slope of a graph at a single point, including an explanation of the formal definition of a derivative, a detailed example of finding a derivative using the definition, and what the derivative equation means and is useful for. Finally, a few examples of finding derivatives of polynomials.