2.11 Implicit Differentiation
By the end of your studying, you should know:
On-screen 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).
An interesting curve first studied by Nicomedes around 200 B.C. is the conchoid, which has the equation x2y2 = (x + 1)2 (4 x2). 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.
ExercisesSee 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 Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Nothing yet has been found. Any ideas?
|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