For the function compute the second-order partial derivatives Fxx,Fyy,Fxy,and fyx (a) f(x,y)=x^2 + Y^3 - 2xy^2  I am new to the subject and id very lost in class.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should evaluate the first order partial derivatives such that:

`f_x(x,y) = 2x - 2y^2`  (notice that y is considered as constant)

`f_y(x,y) = 3y^2 - 4xy`  (notice that x is considered as constant)

You may evaluate the second order partial derivatives such that:

`f_(x x)(x,y) = (del(2x - 2y^2))/(del x)`

`f_(x x)(x,y) = 2`

`f_(xy)(x,y) = (del(2x - 2y^2))/(del y)`

`f_(xy)(x,y) = -4y`

`f_(yy)(x,y) = (del(3y^2 - 4xy))/(del y)`

`f_(yy)(x,y) = 6y - 4x`

`f_(yx)(x,y) = (del(3y^2 - 4xy))/(del x)`

`f_(yx)(x,y) = -4y`

Notice that `f_(xy)(x,y) = f_(yx)(x,y) = -4y.`

Hence, evaluating the partial second order derivatives yields `f_(x x)(x,y) = 2 ; f_(yy)(x,y) = 6y - 4x ; f_(xy)(x,y) = f_(yx)(x,y) = -4y` .

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