130Lec7-2 Partial Derivatives.pdf - 7.2 Partial Derivatives Take the derivative of a function of two variables w.r.t one variable treating the other

# 130Lec7-2 Partial Derivatives.pdf - 7.2 Partial Derivatives...

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Unformatted text preview: 7.2 Partial Derivatives Take the derivative of a function of two variables w.r.t one variable, treating the other variable as a constant. Partial Derivatives (, ) = lim f ( x h, y ) f ( x, y ) h ( Partial derivative ) of w.r.t. (, ) = lim f ( x, y h ) f ( x, y ) h ( Partial derivative ) of w.r.t. h 0 h 0 Subscript Notation for Partial Derivatives Ex) (, ) = (, ) = (, ) (, ) (, ) = 2 3 5 ; find (, ) = (, ) = Ex) (, ) = 2 4 − 7 3 2 − + 2 + 5 (, ) = (, ) = Ex) If (, ) = a. (1, 2) 3 + 2 , find b. (1, 2). Ex) (, ) = 3 4 − 2 , find a. #48 (Page 455) b. BUSINESS: Cobb-Douglas Production Functions A company’s production is given by the Cobb-Douglas function (, ) = 2252/3 1/3 . a. b. c. Find (27, 125) and interpret this number. Find (27, 125) and interpret this number. Which will increase production more: an additional unit of labor or an additional unit of capital? ...
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