This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 deﬁntion 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...
View
Full Document
 Winter '07
 Enright
 Derivative, Fundamental Theorem Of Calculus, Vector Calculus, Vectors, Continuous function, Tangent Hyperplane, Answer Compute

Click to edit the document details