Answer
$g_{xx}=e^{x}-y\times Sin(x)$
$g_{yy}=0$
$g_{xy}=g_{yx}=Cos(x)$
Work Step by Step
$g(x,y)=e^{x}+y\times Sin(x)$
$g_{x}=e^{x}+y\times Cos(x)$
$g_{xx}=e^{x}-y\times Sin(x)$
$g_{yx}=Cos(x)$
$g_{y}=Sin(x)$
$g_{yy}=0$
$g_{xy}=g_{yx}$
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