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Unformatted text preview: Differentiation formulas [1] d (constant) dx = 0 [2] d x n dx = n x n 1 where n ∈ R but n 6 = 0 [3] Derivative of a Sum(Difference) = Sum(Difference) of the Derivatives d ( f ( x ) + g ( x )) dx = d ( f ( x )) dx + d ( g ( x )) dx and d ( f ( x ) g ( x )) dx = d ( f ( x )) dx d ( g ( x )) dx [5] ( k f ( x ) ) = k f ( x ) where k is given real number [6] The Product Rule d dx ( f ( x ) g ( x )) = f ( x ) g ( x ) + f ( x ) g ( x ) [7] The Quotient Rule d dx f ( x ) g ( x ) = f ( x ) g ( x ) f ( x ) g ( x ) ( g ( x )) 2 ——————————————————————————————————– [8] The Power Rule d ( u ( x )) n dx = n ( u ( x )) n 1 · d u ( x ) dx Example Calculate the derivative of ( x 3 1) 5 . Solution Here g ( x ) = ( x 3 1) and n = 5 . d ( x 3 1) 5 dx = 5( x 3 1) 5 1 · d ( x 3 1) dx = 5( x 3 1) 4 (3 x 2 ) [9] The Chain Rule d f ( u ( x )) dx = df ( u ) du · du ( x ) dx Example If f = 5 u 2 + + u + 6 and u ( x ) = ( x 2 + 1)...
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This note was uploaded on 12/12/2011 for the course ECON 101 taught by Professor Bi during the Spring '11 term at York University.
 Spring '11
 bi

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