Unit 2 - Objective 3 - Implicit Differentation

y = 2x² + 6x - 3 is an example where y is an explicit function of x and dy/dx = 4x+6.
On the other hand, x² + y² = 4 has y as an implied function of x. Rather than trying to solve this equation for y and then finding the derivative, we can take the derivative of this equation the way it is. We can do this by remembering that y = u, an implied function of x, and using the chain rule to find the derivative of

Chain Rule

In x² + y² = 4 we first take the derivative of each term.

Then solve for dy/dx (get all the terms which involve dy/dx on one side of the equation then factor it out, and divide through by its coefficient).

Problem 1:

Problem 2:

Problem 3:

This is the slope of the tangent line to the curve at any point. If you pick a point on the curve, you can find the slope of the tangent line to the curve at that point. Say for example, you pick the point (-7,1) on the curve of Example 3. Then the slope of the tangent line would be:

[Unit 2 Outline] [Course Outline] [Home Page]

Copyright © 1996 by B. Chambers and P. Lowry. All Rights Reserved.