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lecture6 - Lecture 6: Partial Derivatives May 12, 2009...

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Unformatted text preview: Lecture 6: Partial Derivatives May 12, 2009 Lecture 6: Partial Derivatives Objectives 1 Define partial derivatives 2 Compute partial derivatives 3 Give a geometric interpretation of partial derivatives 4 Compute higher order partial derivatives. Lecture 6: Partial Derivatives Rate of change, but in which direction? Lecture 6: Partial Derivatives Rate of change, but in which direction? Our ultimate goal is to be able to compute the rate of change in any direction we choose. Lecture 6: Partial Derivatives Derivatives In one dimension f ( x ) = lim h f ( x + h )- f ( x ) h Lecture 6: Partial Derivatives Derivatives In one dimension f ( x ) = lim h f ( x + h )- f ( x ) h In two dimensions we define partial derivatives: f x ( x ) = lim h f ( x + h , y )- f ( x , y ) h f y ( x ) = lim h f ( x , y + h )- f ( x , y ) h Lecture 6: Partial Derivatives Partial Derivatives Idea is to hold one of the variables fixed and compute the rate of change with respect to the other variable....
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lecture6 - Lecture 6: Partial Derivatives May 12, 2009...

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