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Unformatted text preview: Lecture 12 1 Lecture 12: (Sec. 3.1, 3.2) Basic Rules of Differentiation; Product and Quotient Rules Recall: if y = f ( x ) is differentiable, then f ′ ( x ) = d dx [ f ( x )] = Some Basic Rules for Finding Derivatives 1) Derivative of a Constant : If f ( x ) = c for any constant c , then f ′ ( x ) = ex. Find d dx ( − 2) Lecture 12 2 NOTE: If f ( x ) = x , then f ′ ( x ) = parenleftbigg d dx ( x ) = parenrightbigg a54 a45 a63 a27 Proof: 2) The (Simple) Power Rule : If f ( x ) = x n , then f ′ ( x ) = where n is any real number. Lecture 12 3 Find: ex. d dx ( x 165 ) ex. d dx ( 1 x 5 ) ex. d dx ( 5 √ x ) Lecture 12 4 For the following rules, we assume that f and g are differentiable functions of x : 3) The Derivative of a Constant Multiple of a function : If g ( x ) = cf ( x ), then g ′ ( x ) = where c is any constant. We can also say: d dx [ cf ( x )] = Proof : Lecture 12 5 ex. Find f ′ ( x ) for each function: 1) f ( x ) = √ x 3 2) f ( x ) = − 2 5 x 3 Lecture 12 6 4)...
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This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
 Spring '08
 Smith
 Calculus, Derivative, Quotient Rule

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