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Series: Calculus: Some Special Derivatives


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About this Series

  • Lessons: 2
  • Total Time: 0h 33m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 06/23/2009
  • Last Updated At: 07/20/2010

This two part series covers finding the derivatives of the reciprocal and square root functions. In the first lesson, we will calculate the derivative of 1/x (the reciprocal function) using the definition of derivative. As part of this problem, we will review how to find the equation for a line tangent to this function at a particular point. To do this, we'll not only calculate the derivative, but we'll also review the use of the point-slope formula to arrive at the tangent line formula, given the point of tangency and the slope of the line (calculated by the derivative of the curve at the point of tangency).

The second lesson, will show how to calculate the derivative of the square root of x using the definition of the derivative. As part of this problem, we will go through how to calculate the instantaneous rate of change at a given point in time. Further, we'll examine how to use a position function to find the point in time when an object will be moving at a particular instantaneous rate of change (or velocity) by setting the derivative of the position function to that rate of speed and then solving for the variable.

This series is a great review for a CLEP test, mid-term, final exam, or personal growth!

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Calculus. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hôpital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

2174 lessons

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Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

awesome instructional!
~ nachan

This is great lesson if you need to understand using the square root of x in calculus. I love the props he uses to help explain each problem! He also explains how to find the instantaneous rate of change by finding the derivative. He also explains the definition of the derivative and explains a step by step process of finding the problem.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: