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Unformatted text preview: direction of Fow on the map will be in the opposite direction, the direction of steepest descent . The analogue of Remark 3.3.5 for a function of three variables holds for the same reasons. Note that in either case, the gradient lives in the domain of the function; thus, although the graph of a function of two variables is a surface in space, its gradient vector at any point is a vector in the plane. Chain Rules or two dierentiable real-valued functions of a (single) real variable, the Chain Rule tells us that the derivative of the composition is the product of the derivatives of the two functions: d dt V V V V t = t [ f g ] = f ( g ( t )) g ( t ) ....
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- Fall '08