## Implicit Differentiation

Implicit Differentiation
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### Meets NCTM Standards:

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.
Implicit differentiation. The power rule for rational powers.
• What is implicit differentiation?
• How do you take the derivative of x to a fractional exponent?
• How do you take the derivative of the equation for an elipse?
• How do you find the points on an ellipse where the tangent line is horizontal or vertical?
• What is the power rule?
This lesson is a great introduction to implicit differentiation. Several great, complete examples are used, including the equation for an ellipse, and the equation x^3 * y^2 = x * y^3 + 6. Also, in a related topic, you learn how to find dy/dx when y = x^(1/n). You will learn how the power rule works for rational exponents. Some of the examples get pretty long and involved.
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Reviewed by MathVids Staff on December 17, 2008.