Partial Derivatives, Week 4
Partial Derivatives, Week 4 MATH 2232 Multi Variable Calculus
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This 1 page Class Notes was uploaded by Andrew Swann on Tuesday February 17, 2015. The Class Notes belongs to MATH 2232 Multi Variable Calculus at George Washington University taught by Ullman in Spring2015. Since its upload, it has received 38 views.
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Date Created: 02/17/15
Partial Derivatives 1 Notation interpretation 0 dfdX del f over del X 0 D subscript X 0 f sub X 0 f sub 1 2 Interpretation meaning 0 The derivative of Z With respect to X if y is treated as a constant 0 If you increase how much doe Z increasethe ratio 0 3 Computation reduce to single variable 0 Easy 0 Just treat one of the letters as if it is a constant You can even replace it With a number to help 0 4 De nition precision 0 Let g sub y X fXy for Xed y Then D sub X Xy g39 sub y X 0 Given fXy 0 Partial derivatives With respect to X or y Second Partial Derivatives O 0 f sub XX or even f sub yy 0 If it39s positive its concave up 0 Negative concave down 0 Also possible to be f sub Xy or f sub yX O Derivative taken With respect to X then taken With respect to y 0 If negative then there is a type of cork screW effect 0 Clairaut39s theorem f sub Xy and f sub yX are usually the same if they are pretty basic If f has continuous second partial derivatives then true 0 Differentiable apprOXimate by a tangent line simply having partial derivatives does not make a function differentiable 0 If you blew it up a ton then it would follow the tangent line at that point 0 quotHas a tangent planequot
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