Implicit Differentiation
In this lesson on implicit differentiation and derivatives of rational powers, we learn how to find the slope of a curve at any given point, and how to find the points on the curve where the tangent line is either horizontal or vertical. We also explore the power rule for rational powers, and learn how to compute derivatives for functions with fractional exponents. Through various examples and applications, we see how these concepts can be used to solve real-world problems involving curves and functions.
Implicit differentiation. The power rule for rational powers.
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; Rational Powers - Practice with Implicit Differentiation; 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?
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Staff Review
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.
