Unformatted text preview: rule. The function is (625x 2 )1 / 2 , the composition of f ( x ) = x1 / 2 and g ( x ) = 625x 2 . We compute f ± ( x ) = (1 / 2) x3 / 2 using the power rule, and then f ± ( g ( x )) g ± ( x ) =1 2(625x 2 ) 3 / 2 (2 x ) = x (625x 2 ) 3 / 2 . In practice, of course, you will need to use more than one of the rules we have developed to compute the derivative of a complicated function. EXAMPLE 3.11 Compute the derivative of f ( x ) = x 21 x √ x 2 + 1 . The “last” operation here is division, so to get started we need to use the quotient rule ﬁrst. This gives f ± ( x ) = ( x 21) ± x √ x 2 + 1( x 21)( x √ x 2 + 1) ± x 2 ( x 2 + 1) = 2 x 2 √ x 2 + 1( x 21)( x √ x 2 + 1) ± x 2 ( x 2 + 1) ....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Division, Derivative

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