# Chapter10.5 - Chapter 10.5 Page 553 Theorem 1: If f ( x)...

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Chapter 10.5 Page 553 Theorem 1: If c x f = ) ( for some real number c , then 0 ) ( ' = x f Remark: The slope of any horizontal line is zero. Notation: If y is a function of x , then ' y and dx dy are the derivative of the function with respect to x . Page 554 Example 1. (A) If 3 ) ( = x f , then 0 ) ( ' = x f (B) If 4 . 1 - = y , then 0 ' = = dx dy y (D) ( 29 23 dx d Here the function 23 = y = 0 Theorem 2: If = = n x x f n , ) ( a real number, then 1 ) ( ' - = n nx x f . Page 555 Example 2. (A) If 5 ) ( x x f = , then 4 1 5 5 5 ) ( ' x x x f = = - 1

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(B) If 25 x y = , then 24 1 25 25 25 ' x x dx dy y = = = - (D) 3 5 x dx d Here the function 3 5 x y = = 3 2 1 3 5 3 5 3 5 x x = - Example 3 (A) 5 5 1 4 4 4 4 4 4 ) ( ' ) ( 1 ) ( x or x x x f x x f x x f - - = - = = = - - - - . (B) u or u or u u du dy y u y u y 2 1 2 1 2 1 2 1 ' 2 1 2 1 1 2 1 2 1 - - = = = = = . (C) 3 4 3 4 1 3 1 3 1 3 3 1 3 1 3 1 1 x or x x x dx d x dx d - - = - = = -
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## This note was uploaded on 04/09/2008 for the course MAT 220 taught by Professor For during the Spring '08 term at Community College of Allegheny County.

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Chapter10.5 - Chapter 10.5 Page 553 Theorem 1: If f ( x)...

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