Find fxx(x,y), fxy(x,y), fyx(x,y), and fyy(x,y) for the...

Transcript

00:01 In this problem we are given the function f x comma y equal to 2x multiplied by e raised to the power 6x y and for the first part we have to find f f x x of x comma y first we will differentiate the equation the function with respect to x and write f x of x comma y equal to 2 multiplied by x multiplied by e raised to the power 6x y 6y plus e raised to the power 6xy using the product rule of differentiation on simplification we get fx of x comma y equal to 12xy multiplied by e raised to the power 6xy plus 2 multiplied by e raised to the power 6xy now again we will differentiate this with respect to x so we right f x x of x comma y which will be given by 12 multiplied by x y multiplied by e raged to the power 6x y multiplied by 6 6y plus e raise to the power 6 xy plus 2 multiplied by e range to the power 6x y multiplied by 6 y from this we get the value of f x x of x comma y equal to 72 x y square plus 12 plus 12 y multiplied by e to the power 6x y and this is the answer to the first part of the problem next we will find a double differentiation f y y of x comma y first we will differentiate the given function with respect to y and we get 2x multiplied by e raised to the power 6x y multiplied by 6x which will be equal to f y of x comma y equal to 12 x squared multiplied by e raised to the power 6x y now again we will differentiate this equation with respect to y and write f y y y of x comma y is equal to 72 x cube multiplied by e raised to the power 6x 6xy and this is the function f y y of x comma y next to find f x y of x comma y we will differentiate the function f y of x comma y with respect to x so after differentiation we get 12 multiplied by e square sorry x square multiplied by e raised to the power 6x y multiplied by 6x y multiplied by 6x y multiplied by 6 6y plus e raised to the power 6xy multiplied by 2x on simplification we get f xy of x comma y equal to 24 multiplied by 3x square y plus x multiplied by e to the power 6x y and lastly we have to find f y x of x comma y we will get this function by differentiating fx of x comma y with respect to y...

Question

Find $f_{xx}(x,y)$, $f_{xy}(x,y)$, $f_{yx}(x,y)$, and $f_{yy}(x,y)$ for the function $f$. f(x,y) = 6xe^{xy}$ fxx (x,y) = fxy(x,y)= fyx (x,y)= fyy (x,y) =

Question

Find $f_{xx}(x,y)$, $f_{xy}(x,y)$, $f_{yx}(x,y)$, and $f_{yy}(x,y)$ for the function $f$. f(x,y) = 6xe^{xy}$ fxx (x,y) = fxy(x,y)= fyx (x,y)= fyy (x,y) =

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