Learning Outcomes

1. Find the derivative of an implicit function by using implicit differentiation.
2. Use implicit differentiation to determine the equation of a tangent line to an implicit function.

Textbook

• Chapter 3.8  Implicit Differentiation

Textbook Assignment

• p. 317:    300-303 all, 309, 311, 315, 319

WeBWork Assignment

• Derivatives-Implicit

Exit problems of the session

1. Use implicit differentiation to find of the following functions:

(a). (b). 2. Find the equation of the tangent line to the graph of the given equation at the indicated point , .

Key Concepts

• Use implicit differentiation to find derivatives of implicitly defined functions.
• An implicit defined function is a function that the relationship between the function and the variable is expressed by an equation where is not expressed entirely in terms of .
• Implicit differentiation is a technique for computing for a function defined by an equation, accomplished by differentiating both sides of the equation (remember to treat the variable as a function) and solving for #### Videos and Practice Problems of Selected Topics

1. Implicit differentiation  (8:01) A discussion on the implicit derivative of the unit circle .
2. An example (4:55) Implicit differentiation of .
3. An example (5:24) Find the slope of the tangent line to the curve at using implicit differentiation.
4. * Practice: Find implicitly. (4 problems)