MAT 1221 Survey of Calculus Section 2.5 The Chain Rule

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Presentation transcript:

MAT 1221 Survey of Calculus Section 2.5 The Chain Rule

Expectations Use equals signs Pay attention to units Problem 2: Formally answer the question

Reminder Exam 1, next Monday Look at the comments from the grader Look at the solutions online Make improvements

Preview We know how to find derivatives of Power functions, polynomials, products, quotients. Section 2.5: Composite functions We will look at the chain rule. Focus on the special case : Extended Power Rule

Recall (Composite Functions) Suppose

Recall (Composite Functions) Suppose Then,

The Chain Rule: Part I

The Chain Rule: Part II Version 1 Meaning Find and then substitute Multiply by

The Chain Rule: Part II Version 2

Special Case: Extended Power Rule u

u

u

Example 1

u

Expectations Must show the “formula” step when using the Chain Rule/ Extended Power Rule

Example 2

u

Example 3 (With Product Rule)

Example 4 (With Quotient Rule)