http://i33.tinypic.com/2wce634.png

I did the first part by the definition of total derivative, but can not think of the way to do the second part of the question. Any help please?

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- October 25th 2009, 05:35 AM6DOMTotal Derivative and Orthogonality
http://i33.tinypic.com/2wce634.png

I did the first part by the definition of total derivative, but can not think of the way to do the second part of the question. Any help please? - October 25th 2009, 07:29 AMOpalg
If then for all x in U. Differentiate that equation.

- October 25th 2009, 08:24 AM6DOM
- October 25th 2009, 11:10 AMOpalg
I meant differentiate with respect to x, using the chain rule. I suppose I should have used t rather than x, since the question says that f is a function of t. Then evaluated at t=a is equal to , and similarly for the other coordinates. The result of differentiating both sides of the equation in that way ought to remind you of an inner product.

- October 25th 2009, 11:22 AM6DOM