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lecture6

# lecture6 - Lecture 6 Partial Derivatives Lecture 6 Partial...

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Lecture 6: Partial Derivatives May 12, 2009 Lecture 6: Partial Derivatives

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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

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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 0 ( x ) = lim h 0 f ( x + h ) - f ( x ) h Lecture 6: Partial Derivatives

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Derivatives In one dimension f 0 ( x ) = lim h 0 f ( x + h ) - f ( x ) h In two dimensions we define partial derivatives: f x ( x ) = lim h 0 f ( x + h , y ) - f ( x , y ) h f y ( x ) = lim h 0 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. Lecture 6: Partial Derivatives

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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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