section37_material

section37_material - MATH110BUSINESSCALCULUS

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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 32 0 43 0 () ( ) ( ) , ( ) lim 1 ( ) ( ) ( ) lim 2 ( ) ( ) ( ) lim 3 ( ) ( ) ( ) lim 4 ... h h h h fx h fx fx x f x h f xx f x x h f f x x h f 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!
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Theorem: The Power Rule If n is any constant and () n f xx = , then 1 n f xn x = Examples: 76 If ( ) , by the Power Rule we have ( ) 7 f f x x == More Exercises: Find the derivative of each of the following function: 1. 10 f = 2. 2 1 fx x = 3. f = 4. 1 f = 5. () 1 = 6. 4.8 f =
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Theorem: Derivatives of Sums, Differences, and Constant Multiples If () f x and g x are any two differentiable functions, and if c is any constant, then the functions f x g x ± and c f x are differentiable, and
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This note was uploaded on 10/19/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.

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section37_material - MATH110BUSINESSCALCULUS

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