Lesson 7 Derivative using formulas

Lesson 7 Derivative using formulas - DIFFERENTIATION OF...

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DIFFERENTIATION OF ALGEBRAIC FUNCTIONS
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OBJECTIVES : to identify the different rules of differentiation and distinguish one from the other; prove the different rules of differentiation using the increment method; find the derivative of an algebraic function using the basic rules of differentiation; and extend these basic rules to other “complex” algebraic functions.
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DERIVATIVE USING FORMULAS The increment-method (four-step rule) of finding the derivative of a function gives us the basic procedures of differentiation. However these rules are laborious and tedious when the functions to be differentiated are “complex”, that is, functions with
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Understanding of the theorems of differentiation is very important. This is the heart of differential calculus. All of the succeeding topics such as applications of derivatives, differentiation of transcendental functions etc. will be dependent on these theorems. Understanding of
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DIFFERENTIATION FORMULAS Derivative of a Constant Theorem: The derivative of a constant function is 0; that is, if c is any real number, then 0 ] [ = c dx d
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DIFFERENTIATION FORMULAS Derivatives of Power Functions Theorem: ( Power Rule) If n is a positive integer, then 1 ] [ - = n n nx x dx d In words, to differentiate a power function,
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