Copy_of_3.3notestouse

# Copy_of_3.3notestouse - The Product Rule uv ( ) = The...

This preview shows pages 1–4. Sign up to view the full content.

Calculus Section 3.3 Page15 3.3 Rules for Differentiation Basic Rules Derivative of a Constant c ( ) = Power Rule x n ( ) = Constant Multiple Rule c u ( ) = Sum and Difference Rule u ± v ( ) = Example 1 Differentiating using the basic rules Find dy dx if a) y = x 3 + 6 x 2 - 5 3 x + 16 b) y = x 4 4 + x 2 8 + 5 x c) y = 5 x 2 + 1 x - 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Calculus Section 3.3 Page 16 d) y = x + 3 x - 1 e) y = x 2 + 3 2 x Example 2 Finding Tangent Lines Use the results from part e) to find the equation of the tangent to the curve y = x 2 + 3 2 x at the point 1,2 ( ) . Support your answer graphically. Example 2 Finding Horizontal Tangents a) Does the curve y = x 4 - 2 x 2 + 2 have any horizontal tangents? If so, where?
Calculus Section 3.3 Page17 b) Determine the x -values where the curve y = 0.2 x 4 - 0.7 x 3 - 2 x 2 + 5 x + 4 has horizontal tangents. More Differentiation Rules

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The Product Rule uv ( ) = The Quotient Rule u v = Example 3 Differentiating a Product Find f x ( ) if f x ( ) = x 2 + 1 ( ) x 3 + 3 ( ) Example 5 Working With Numerical Values Let y = uv be the product of the functions u and v. Find y 2 ( ) if u 2 ( ) = 3, u 2 ( )= -4, v 2 ( )= 1, and v 2 ( ) = 2 Example 6 Differentiating a Quotient Differentiate f x ( ) = x 2-1 x 2 + 1 Calculus Section 3.3 Page 18 Example 7 Second and Higher Order Derivatives Find the first four derivatives of y = x 3-5 x 2 + 2 Assignment II3 Page 120 121 #1 12 all, 13, 14, 16, 17, 18, 23 31 odd, 34...
View Full Document

## This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at St. Michael.

### Page1 / 4

Copy_of_3.3notestouse - The Product Rule uv ( ) = The...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online