 Created By Ms. Kondo

 Description:
Like people, mathematical relations are not always explicit about their intentions. In this tutorial, we'll be able to take the derivative of one variable with respect to another even when they are implicitly defined (like "x^2 + y^2 = 1").  Purpose:
Students will:
• Explore relations describing implicit functions.
• Differentiate implicitly.  Targets: Student
 APS.MA.912.II.F.3
 9th Grade, 10th Grade, 11th Grade, 12th Grade
 Implicit differentiation

This video uses the circle example (similar to the one we did in class) to explain an easier way to find the derivative (using implicit differentiation).

 Showing explicit and implicit differentiation give same result

This video compares the traditional method of taking the derivative (y alone) and the method we’ve just learned, implicit differentiation. You could use either method in this example, which one is easier?

 Implicit derivative of (xy)^2=x+y1

Example of how to use implicit differentiation. It might be good for you to try this problem first yourself, then watch Khan’s tutorial on how he completes it.

 Implicit derivative of y=cos(5x3y)

Example of how to use implicit differentiation. It might be good for you to try this problem first yourself, then watch Khan’s tutorial on how he completes it.

 Implicit derivative of (x^2+y^2)=5x^2y^2

Example of how to use implicit differentiation. It might be good for you to try this problem first yourself, then watch Khan’s tutorial on how he completes it.

 Finding slope of tangent line with implicit differentiation

Example of how to use implicit differentiation. It might be good for you to try this problem first yourself, then watch Khan’s tutorial on how he completes it. This video reminds us of the connection between the derivative and the slope of the tangent line!

 Implicit derivative of e^(xy^2)=xy

Example of how to use implicit differentiation. It might be good for you to try this problem first yourself, then watch Khan’s tutorial on how he completes it.

 Assessment: Implicit differentiation

How well have you mastered implicit differentiation? Find out by completing this assessment!
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