lecture19 - f ( x ) = v ( x ) u ( x )-u ( x ) v ( x ) ( v (...

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Math 006 (Lecture 19) Product Rule Theorem 1. (Product Rule) If y = f ( x ) = F ( x ) G ( x ) , then f 0 ( x ) = F ( x ) G 0 ( x ) + F 0 ( x ) G ( x ) . Example 1. Find the derivative of (a) f ( x ) = 2 x 2 (3 x 4 - 2) (b) y = ( x + 1)( 1 x - 1) Example 2. Let f ( x ) = (2 x - 9)( x 2 + 6) (a) Find f 0 ( x ) (b) Find the equation of the tangent line at x = 3 (c) Find the values of x where the tangent line is horizontal. 1
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Quotient Rule Theorem 2. (Quotient Rule) If y = f ( x ) = u ( x ) v ( x ) , then dy dx =
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Unformatted text preview: f ( x ) = v ( x ) u ( x )-u ( x ) v ( x ) ( v ( x )) 2 . Example 3. Find the derivative of each of the following functions: (a) f ( x ) = x 2 x 2-1 (b) f ( t ) = t 2-t t 3 + 1 (c) y = x 3 x 2 + 3 x + 4 (d) f ( x ) = 3 √ x x 2-3 (e) f ( x ) = 2 x-1 ( x 3 + 2)( x 2-3) 2...
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This note was uploaded on 09/04/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture19 - f ( x ) = v ( x ) u ( x )-u ( x ) v ( x ) ( v (...

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