Problems_partial derivatives 021211 - Copy

Problems_partial derivatives 021211 - Copy - Problem #3:...

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Problem #3: partial derivatives of f(x; y) = (3x 5y + 8) Solve: y x y x f 15 ) , ( = ; x y y x f 15 ) , ( = Explanation: If f = ax n , then 1 - = n nax x f , where a is a constant. A derivative of a non- variable (e.g., a constant number) is equal to zero. As it is a partial derivative, for x f , y is considered as a constant, and vice versa. Problem #4: partial derivatives of f(x; y) =x^2+y/x+3 Solve: 2 2 ) , ( x y x x y x f - = ; x y y x f 1 ) , ( = Explanation: same formula as above. g(x)= 1/x = x -1 , thus, g(x)’=(-1)x -1-1 = - 1x -2 = -1/x 2 (Note: g(x)’ is a shorthand for x f ) Problem #5: partial derivatives of f(x,y) = xe^-2xy Solve: xy xy e y x e x y x f 2 2 ) 2 ( ) , ( - - - + = ; xy e x y y x f 2 2 2 ) , ( - - = Explanation: (1) For a compounded function such as f(x) = g(x)h(x),
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Problems_partial derivatives 021211 - Copy - Problem #3:...

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