{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

section37_material

# section37_material - Section 3.7 Derivatives of Powers Sums...

This preview shows pages 1–5. Sign up to view the full content.

MATH 110 BUSINESS CALCULUS CHAPTER 3 INTRODUCTION TO THE DERIVATIVE Section 3.7 Derivatives of Powers, Sums, and Constant Multiples Suppose we were to find a derivative of each of the following functions using the limit: 0 2 0 3 2 0 4 3 0 ( ) ( ) ( ) , ( ) lim 1 ( ) ( ) ( ) , ( ) lim 2 ( ) ( ) ( ) , ( ) lim 3 ( ) ( ) ( ) , ( ) lim 4 ... h h h h f x h f x f x x f x h f x h f x f x x f x x h f x h f x f x x f x x h f x h f x f x x f x x h + = = = + = = = + = = = + = = = See something interesting? A pattern? Once a pattern is recognized and established (proved), we can rely on it to find the derivatives of other functions. Thus, we develop a technique!

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

View Full Document
Theorem: The Power Rule If n is any constant and ( ) n f x x = , then 1 ( ) n f x nx = Examples: 7 6 If ( ) , by the Power Rule we have ( ) 7 f x x f x x = = More Exercises: Find the derivative of each of the following function: 1. 10 ( ) f x x = 2. 2 1 ( ) f x x = 3. ( ) f x x = 4. 1 ( ) f x x = 5. ( ) 1 f x = 6. 4.8 ( ) f x x =
Theorem: Derivatives of Sums, Differences, and Constant Multiples If ( ) f x and ( ) g x are any two differentiable functions, and if

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.

{[ snackBarMessage ]}