Find the second-order partial derivatives of the given function. In each case, show that the mixed partial derivatives [tex]f_{xy}[/tex] and [tex]f_{yx}[/tex] are equal.(adsbygoogle = window.adsbygoogle || []).push({});

Function:

[tex]f(x,y)=x^{3}+x^{2}y+x+4[/tex]

My work (Correct me if I am wrong):

[tex]\frac{\partial{f}}{\partial{x}}}=3x^{2}+2xy+1[/tex]

[tex]\frac{\partial{f}}{\partial{y}}}=x^{2}[/tex]

[tex]f_{xx}=6x+2y[/tex]

[tex]f_{yy}=0[/tex]

[tex]f_{xy}=6x+2y[/tex]

[tex]f_{yx}=0[/tex]

If I am correct, which I am probably not, how could [tex]f_{xy}[/tex] possibly be equal to [tex]f_{yx}[/tex]? Shouldn't that always be true anyways? If that's so, then obviously I messed up somewhere. Please help!

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# Homework Help: Need help on a partial derivative problem!

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