This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 3. Di ff erentiation 3.3 Di ff erentiation Rules Derivative of a Constant Function. If f has the constant value f ( x ) = c , then df dx = d dx [ c ] = 0 . Proof. From the definition: f ( x ) = lim h → f ( x + h ) f ( x ) h = lim h → o c c h = lim h → 0 = 0 . QED Power Rule for Positive Integers If n is a positive integer, then d dx [ x n ] = nx n 1 . Note. Before we present the proof of the Power Rule, we introduce the Binomial Theorem. Theorem. Binomial Theorem Let a and b be real numbers and let n be a positive integer. Then ( a + b ) n = a n + na n 1 b + n ( n 1) 2 a n 2 b 2 + . . . + nab n 1 + b n = n i =0 n i a n i b i where n i = n ! ( n i )! i ! and i ! = ( i )( i 1)( i 2) · · · (3)(2)(1) . Note. We can prove the Binomial Theorem using Mathematical Induc tion ....
View
Full
Document
This note was uploaded on 03/18/2011 for the course MATH 032 taught by Professor Junghenn during the Fall '08 term at GWU.
 Fall '08
 JUNGHENN
 Calculus, Derivative

Click to edit the document details