lecture18hout

lecture18hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 18) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 11 Outline 1 Power Rule 2 Basic Differentiation Properties Albert Ku (HKUST) MATH 006 2 / 11 Power Rule Finding Derivatives using Differentiation Rules Given a function f ( x ), the most primitive way to compute its derivative is to evaluate the limit of its difference quotient, which may be quite difficult if f ( x ) is a complicated expression in x . Therefore, we will develop some differentiation rules to facilitate the computation of derivatives. They are Power rule Product rule Quotient rule Chain rule Albert Ku (HKUST) MATH 006 3 / 11 Power Rule Power Rule In this lecture, we will learn the first and the most basic differentiation rule- Power rule: Theorem (Power Rule) If y = f ( x ) = x n where n is a real number, then f ( x ) = nx n- 1 . Albert Ku (HKUST) MATH 006 4 / 11 Power Rule Example Find f ( x ) for each of the following functions: (a) f ( x ) = 3 (More generally,...
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This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture18hout - MATH 006 Calculus and Linear Algebra...

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