Unformatted text preview: x 2 ) d dx x 2 = 2 x cos( x 2 ) , so Z 2 x cos( x 2 ) dx = sin( x 2 ) + C. Even when the chain rule has “produced” a certain derivative, it is not always easy to see. Consider this problem: Z x 3 p 1x 2 dx. There are two factors in this expression, x 3 and √ 1x 2 , but it is not apparent that the chain rule is involved. Some clever rearrangement reveals that it is: Z x 3 p 1x 2 dx = Z (2 x ) ±1 2 ¶ (1(1x 2 )) p 1x 2 dx....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Derivative, Inverse function, Inverse trigonometric functions, dx

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