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Unformatted text preview: y ) f ( x, y ) y y t . Upon taking limits, we nd that dz dt = lim t f ( x + x, y ) f ( x, y ) x x t + f ( x, y + y ) f ( x, y ) y y t = f x dx dt + f y dy dt . This is called the total derivative of the function z = f ( x, y ). Note that it involves partial derivatives . This formula is the same as the more familiar result involving the dot product of the gradient: dz dt = ( f ) ( t ) in terms of f ( x, y ) = f x , f y . Upon multiplying both sides by the dierential dt we nd the total dierential above....
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue University-West Lafayette.
- Spring '09