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Unformatted text preview: x ) = R a x f ( t ) dt. Then d dx g ( x ) =f ( x ) . (b) Suppose f ( x, y, z ) = ( y, x, z ) . Then the total derivative is 1 1 1 . Answer (a) is true. This follows from the fundamental theorem of calculus: d dx Z a x f ( t ) dt =d dx Z x a f ( t ) dt =f ( x ) . (b) is also true. This follows from the dention of the total derivative: If f ( x, y, z ) = ( f 1 ( x, y, z ) , f 2 ( x, y, z ) , f 3 ( x, y, z )) (as in the setup of this problem), then D ( f ) = f 1 x f 1 y f 1 z f 2 x f 2 y f 2 z f 3 x f 3 y f 3 z . In this case of the problem, this is 1 1 1 . 2...
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 Winter '07
 Enright
 Vector Calculus, Vectors

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