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Determine the largest subset of 3 on which the given vector field is differentiable. F = ( x 2 y 2 z 2 + 6

Determine the largest subset of
3
on which the given vector field is differentiable.
F =
(x2 y2 z2+6)4/3, x cos(yz),
xy9 z2
{(x, y, z) in 3| z 3}
{(x, y, z) in 3| x2+ y2+ z2>6}
{(x, y, z) in 3| z 9}
{(x, y, z) in 3| xy 0}
{(x, y, z) in 3| x2+ y2+ z2<6}

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