Question 26.1: If v = 3x²yi + 2xyzj − 3x^4y²k, find  ∂v / ∂x , ∂v / ∂y , ∂v......

We find

{\frac{\partial{\bf{v}}}{\partial x}}=6x{y}\mathbf{i}+2y z\mathbf{j}-12x^{3}y^{2}\mathbf{k}

{\frac{\partial{\bf{v}}}{\partial y}}=3x^{2}\mathbf{i}+2x z\mathbf{j}-6x^{4}y\mathbf{k}

{\frac{\partial\mathbf{v}}{\partial z}}=2xy\mathbf{j}

{\frac{\partial^{2}\mathbf{v}}{\partial x^{2}}}=6y\mathbf{i}-36x^{2}y^{2}\mathbf{k}

{\frac{\partial^{2}\mathbf{v}}{\partial x\partial z}}=2y\mathbf{j}