The Derivative
4359 views
|
2
ratings
Lesson Description:
Slope of the tangent line; definition of the derivative. Differentiability and non-differentiability at a point.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Additional Resources:
- Derivatives and Differentiation - Practice with Derivatives and Differentiation.
- Tangent Lines and Normal Lines - Practice problems with Tangent Lines and Normal Lines.
- Differentiability and Continuity - Practice problems on Differentiability and Continuity.
- 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
Questions answered by this video:
- What is a derivative?
- How do you find the slope of a curve?
- How do you find the slope of a tangent line at a point on a curve?
- What is the definition of a derivative?
- What does the graph of the derivative function look like?
- How do you find a derivative using the formal definition of a derivative?
- What is a corner point?
- What is a cusp?
- When is a function non-differentiable?
- How do you sketch the graph of f'(x)?
-
Staff Review
This video explains what a derivative is carefully and precisely. Math terms are used, which can at times make this video difficult for a beginning Calculus student to follow. However, this video is very accurate and a good, complete explanation of a derivative. A very cool animation is included, which really brings home the idea of the graph of the derivative of a function.
![[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)
