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lect12_3

# lect12_3 - Partial Derivatives(12.3 1 Partial Derivatives...

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Partial Derivatives - (12.3) 1. Partial Derivatives Recall f ! ! x " " lim h # 0 f ! x \$ h " ! f ! x " h provided the limit exists. The derivative of f describes the rate of change of f along the x -axis. Now we like to consider the rates of change of a function in two variables along the x -axis and the y -axis. 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 # 0 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 # 0 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 constants. All differentiation rules for functions in one variable apply here.

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lect12_3 - Partial Derivatives(12.3 1 Partial Derivatives...

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