Lect14 - Recall f ( x) = x f ( x ) = 1 f ( x ) = 2 x f ( x...

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92.131 Lecture 14 1 of 11 Ronald Brent © 2008 All rights reserved. Recall x x f = ) ( 1 ) ( = x f 2 ) ( x x f = x x f 2 ) ( = 3 ) ( x x f = 2 3 ) ( x x f = 1 1 ) ( = = x x x f 2 2 ) 1 ( 1 ) ( = = x x x f And 2 2 1 ) ( = = x x x f 3 3 ) 2 ( 2 ) ( = = x x x f See the pattern? To take the derivative of k x , multiply down the k then subtract one from the exponent.
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92.131 Lecture 14 2 of 11 Ronald Brent © 2008 All rights reserved. Theorems for Calculating Derivatives Theorem: (Power rule for derivatives) Let k be any real constant. If k x x f = ) (, t h e n 1 ) ( = k x k x f . Theorem: (The constant multiple rule for derivatives) Let k be a real constant, and ) ( x f be a differentiable function, and let ) ( ) ( x f k x g = . Then ) ( ) ( ) ( ) ( x f k x f k x g = = . Theorem: (The sum rule for derivatives) Let ) ( x f and ) ( x g be differentiable functions, and let ) ( ) ( ) ( x g x f x h + = . Then ) ( ) ( ) ( ) ( ) ( x g x f x g f x h + = + = . Theorem: (The difference rule for derivatives) Let ) ( x f and ) ( x g be differentiable functions, and let ) ( ) ( ) ( x g x f x h = . Then ) ( ) ( ) ( ) ( ) ( x g x f x g f x h = = .
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92.131
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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Lect14 - Recall f ( x) = x f ( x ) = 1 f ( x ) = 2 x f ( x...

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