lecture17 - Math 121 Lecture 17 Chapter 3 Techniques of...

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Chapter 3 Techniques of Differentiation Math 121 Lecture 17 ! The Product and Quotient Rules ! The Chain Rule and the General Power Rule ! Implicit Differentiation and Related Rates
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§ 3.1 The Product and Quotient Rules ! The Product Rule ! The Quotient Rule ! Rate of Change
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Differentiate the function. Let and . Then, using the product rule, and the general power rule to compute g ! ( x ), g x ( ) = x 2 " 3 ( ) 10 d dx x 2 + 3 ( ) x 2 " 3 ( ) 10 [ ] = x 2 + 3 ( ) # d dx x 2 " 3 ( ) 10 [ ] + x 2 " 3 ( ) 10 # d dx x 2 + 3 ( ) = x 2 + 3 ( ) " 10 x 2 # 3 ( ) 9 " d dx x 2 # 3 ( ) + x 2 # 3 ( ) 10 " 2 x = x 2 + 3 ( ) " 10 x 2 # 3 ( ) 9 " 2 x + x 2 # 3 ( ) 10 " 2 x .
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Remember the poem ‘lo d hi minus hi d lo square the bottom and away you go’ This poem is the mnemonic for the taking the derivative of a quotient. Differentiate. Let and . Then, using the quotient rule x + 2 x 2 + 1 f x ( ) = x + 2 g x ( ) = x 2 + 1 d dx x + 2 x 2 + 1 " # $ % = ( x 2 + 1) ( d dx x + 2 ( ) ) x + 2 ( ) ( d
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lecture17 - Math 121 Lecture 17 Chapter 3 Techniques of...

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