MAT 1234 Calculus I Section 3 8 Implicit

MAT 1234 Calculus I Section 3. 8 Implicit Differentiation http: //myhome. spu. edu/lauw

Next… l l Web. Assign 2. 6 Quiz on 2. 5, 2. 6. Be sure to prepare for it. Remember, good study skills help you to do well in exams.

Web. Assign Reminder l l Be sure to simplify your answers. Web. Assign accepts un-simplified answers.

Preview l l Introduce a new form of extended power rule (notations changes) Introduce Implicit Differentiation

Recall (Extended Power Rule)

Recall (Extended Power Rule)

Recall (Extended Power Rule)

Recall (Extended Power Rule)

Recall (Extended Power Rule) l l If y is a function in x, then

Recall (Extended Power Rule) l

Example 0

The Needs for Implicit Differentiation…

Example 1 l l Find the slopes of the tangent line on the graph i. e. find y x

Example 1: Method I Make y as the subject of the equation: y x

Example 1: Method I Make y as the subject of the equation: y x

Example 1: Method I Make y as the subject of the equation: y x

Example 1: Method I Suppose the point is on the upper half circle y x

Example 1: Method I Suppose the point is on the lower half circle y x

Example 1: Method I l 1. 2. Two disadvantages of Method I: ? ? ?

Example 1: Method II Implicit Differentiation: Differentiate both sides of the equation.

Expectation l You are required to show the implicit differentiation step

Notations l

Example 2

Example 3 Find the slope of the tangent line at .

Notations Correct Incorrect because or

Example 4