You could also use a package that I wrote for that purpose

https://continuum-mechanics.readthedocs.io/en/latest/

If you are interested in Cartesian coordinates only you could just do the 
following

u = Matrix([x, 2*y*z, 3*x*y])
J = u.jacobian([x, y, z])
H = Array([J[:, k].jacobian([x, y, z]) for k in range(3)], (3, 3, 3))

to get

[[0  0  0]  [0  0  0]  [0  0  0]]
[[       ]  [       ]  [       ]]
[[0  0  0]  [0  0  2]  [0  2  0]]
[[       ]  [       ]  [       ]]
[[0  3  0]  [3  0  0]  [0  0  0]]



On Friday, July 3, 2020 at 6:24:44 PM UTC-5, Isaque Soares wrote:
>
> Is there a way to compute the gradient and hessian matrices of a vector 
> field like u = (x) i + (2yz) j + (3xy) k.
>

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