Introduction to Derivatives
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.
- Lesson Slides - Slides that are written on from the lesson.
- Table of Derivatives - Table of derivatives of several different functions.
- Differentiation Identities - Limit definitions of the derivative, Fundamental Theorem for Derivatives, and rules of derivatives
- What is a derivative?
- How do you take a derivative?
- What is Calculus?
-
Staff Review
Have you ever just wondered, what is a derivative? Do you want to understand what it means to find a derivative, both practically and conceptually? This video explains concisely what a derivative means to those of you who have very little background of Calculus. It's also a great refresher if you are having trouble at the beginning of your Calculus course. You won't find any resources here, however. -
-
-
![[C.2] Numerical Derivative preview image](https://www.mathvids.com/rails/active_storage/representations/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaHBBbHNIIiwiZXhwIjpudWxsLCJwdXIiOiJibG9iX2lkIn19--c6ee1ea56bbd5c901b61139448f10be109cf4c25/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaDdCam9VY21WemFYcGxYM1J2WDJ4cGJXbDBXd2RwQVpacGN3PT0iLCJleHAiOm51bGwsInB1ciI6InZhcmlhdGlvbiJ9fQ==--fd851aaa3027f3a83a588ba5d0f1fd585b3d8659/%5Bc.2%5D%20numerical%20derivative.jpg)
![[C.3] Elasticity preview image](https://www.mathvids.com/rails/active_storage/representations/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaHBBbHdIIiwiZXhwIjpudWxsLCJwdXIiOiJibG9iX2lkIn19--d21bd33a1c06e3acc8f7fac2b42d3a75574eaedf/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaDdCam9VY21WemFYcGxYM1J2WDJ4cGJXbDBXd2RwQVpacGN3PT0iLCJleHAiOm51bGwsInB1ciI6InZhcmlhdGlvbiJ9fQ==--fd851aaa3027f3a83a588ba5d0f1fd585b3d8659/%5Bc.3%5D%20%20elasticity.jpg)
