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z=xy^2+ysin^2(x+y)
∂z/∂x=y^2+2ysin(x+y)cos(x+y)=y^2+ysin(2x+2y)
∂z/∂y=2xy+sin^2(x+y)+2ysin(x+y)cos(x+y)=2xy+sin^2(x+y)+ysin(2x+2y)
∂²z/∂x²=2ycos(2x+2y)
∂²z/∂y²=2x+2sin(x+y)cos(x+y)+sin(2x+2y)+2ycos(2x+2y)
=2x+2sin(2x+2y)+2ycos(2x+2y)
∂²z/∂x∂y=2y+sin(2x+2y)+2ycos(2x+2y)
∂z/∂x=y^2+2ysin(x+y)cos(x+y)=y^2+ysin(2x+2y)
∂z/∂y=2xy+sin^2(x+y)+2ysin(x+y)cos(x+y)=2xy+sin^2(x+y)+ysin(2x+2y)
∂²z/∂x²=2ycos(2x+2y)
∂²z/∂y²=2x+2sin(x+y)cos(x+y)+sin(2x+2y)+2ycos(2x+2y)
=2x+2sin(2x+2y)+2ycos(2x+2y)
∂²z/∂x∂y=2y+sin(2x+2y)+2ycos(2x+2y)
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