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Unformatted text preview: Partial Derivatives  (12.3) 1. Partial Derivatives Recall f ! ! x " " lim h # f ! x $ h " ! f ! x " h provided the limit exists. The derivative of f describes the rate of change of f along the xaxis. Now we like to consider the rates of change of a function in two variables along the xaxis and the yaxis. Partial derivatives of a function in 2 variables: Definition of a partial derivative of a function: The partial derivative of f ! x , y " with respect to x , written by " f " x , is defined by " f " x ! x , y " " lim h # f ! x $ h , y " ! f ! x , y " h provided the limit exists. The partial derivative of f ! x , y " with respect to y , written by " f " y , is defined by " f " y ! x , y " " lim h # f ! x , y $ h " ! f ! x , y " h provided the limit exists. Other notations of partial derivatives: z " f ! x , y " " f " x , " z " x , f x , z x ; " f " y , " z " y , f y , z y A partial derivative is a derivative of a function with respect to one variable as other variables are treated as...
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This note was uploaded on 02/05/2012 for the course MATH 2142 taught by Professor Lerna during the Fall '10 term at FIU.
 Fall '10
 Lerna
 Derivative, Rate Of Change

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