The electric potential at a point \[(x,\text{ }y,\text{ }z)\] is given by \[V=-{{x}^{2}}\,y-x{{z}^{3}}+4\] The electric field \[\vec{E}\] at that point is [AIPMT (S) 2009]

• A. \[\vec{E}=\hat{i}\,(2xy+{{z}^{3}})+\hat{j}\,{{x}^{2}}+\hat{k}\,3x{{z}^{2}}\]
• B. \[\vec{E}=\hat{i}\,2xy+\hat{j}({{x}^{2}}+{{y}^{2}})+\hat{k}\,(3xz-{{y}^{2}})\]
• C. \[\vec{E}=\hat{i}\,{{z}^{3}}+\hat{j}\,xyz+\hat{k}\,{{z}^{2}}\]
• D. \[\vec{E}\,=\,\hat{i}\,(2xy-{{z}^{3}})+\hat{j}\,x{{y}^{2}}+\hat{k}\,3{{z}^{2}}x\]