2.3 ProductQuotientRule

# 2.3 - MAC2233 North MDC 2.3Product&QuotientRules; ProductRule:Iff(x)andg(x),(x)=f(x)g(x)and d d d f x g x = f x g x g x f x or(fg)=fg gf; fgisf dx d

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MAC2233 MDC- North 2.3 Product & Quotient Rules; Higher-Order Derivatives Product Rule:   If  f(x)  and  g(x)   are differentiable at  x , then so is their product   P(x) = f(x) g(x)   and         ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 d d d f x g x f x g x g x f x dx dx dx = +  or  (fg)’ = fg’ + gf ’ ; the derivative of the product  fg  is  times the derivative of  g  plus  g  times the derivative of  f . Quotient Rule:   If  f(x)  and  g(x)   are differentiable functions, then so is their quotient   Q(x) = f(x)/ g(x)  and         ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 , d d g x f x f x g x f x d dx dx g x dx g x g x - = 2 0  or  ' ' ' f gf fg g g - = ÷ 2 Second derivative  is the derivative of the derivative.  If  y = f(x) , the second derivative is denoted by

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## This note was uploaded on 01/04/2012 for the course MAC 2233 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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2.3 - MAC2233 North MDC 2.3Product&QuotientRules; ProductRule:Iff(x)andg(x),(x)=f(x)g(x)and d d d f x g x = f x g x g x f x or(fg)=fg gf; fgisf dx d

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