2.11 Implicit Differentiation

By the end of your studying, you should know:
Onscreen applet instructions:
The button at the very bottom gives the interval over which you are tracing where it is possible to define y as a function of x. Use this button only to check your work after you have tried to find the interval on your own.
ExamplesFind y' by implicit differentiation, where xy = cot(xy).
Find the tangent line to the ellipse
An interesting curve first studied by Nicomedes around 200 B.C. is the conchoid, which has the equation x^{2}y^{2} = (x + 1)^{2} (4 – x^{2}). Use implicit differentiation to find a tangent line to this curve at the point (–1, 0).
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.11 Implicit Differentiation (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
Implicit Differentiation

Interesting Application
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2.10 The Mean Value Theorem  Table of Contents  2.12 Derivatives of Exponential and Logarithm Functions 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel