Chap3_Sec2

# Chap3_Sec2 - Example 5 Dont use the Quotient Rule every...

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a. If f ( x ) = xe x , find f ’ ( x ). b. Find the n th derivative, f ( n ) ( x ) THE PRODUCT RULE Example 1 (3.2)

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Differentiate the function In two ways: -Using the Product Rule. -Using the Power Rule. THE PRODUCT RULE Example 2 (3.2) ( ) ( ) f t t a bt = +
If , where g (4) = 2 and g’ (4) = 3, find f’ (4). THE PRODUCT RULE Example 3 (3.2) ( ) ( ) f x xg x =

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Let Find y’. 2 3 2 6 x x y x + - = + THE QUOTIENT RULE Example 4 (3.2)
Find an equation of the tangent line to the curve y = e x / (1 + x 2 ) at the point (1, ½ e ). THE QUOTIENT RULE Example 5 (3.2)

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In the figure, notice that the function is increasing and crosses its tangent line at (1, ½ e ). THE QUOTIENT RULE

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Unformatted text preview: Example 5 Dont use the Quotient Rule every time you see a quotient. s Sometimes, its easier to rewrite a quotient first to put it in a form that is simpler for the purpose of differentiation. Find the derivative of NOTE 2 3 2 ( ) x x F x x + = Heres a summary of the differentiation formulas we have learned so far. ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 ' 2 ' ' ' ' ' ' ' ' ' ' ' ' ' n n x x d d d c x nx e e dx dx dx cf cf f g f g f g f g f gf fg fg fg gf g g-= = = = + = +-=- -= + = DIFFERENTIATION FORMULAS...
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## This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

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Chap3_Sec2 - Example 5 Dont use the Quotient Rule every...

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