Regarding the derivation of the Hessian matrix for f(q) in the file "notebooks_2023 lecture14.pdf,"

[wenchenwan]

Regarding how the Hessian matrix of f(q) is derived in the file "notebooks_2023 lecture14.pdf," as shown in the figure, is there anyone familiar with this who can provide an explanation? It would be greatly appreciated if the derivation process could be shared. Thank you very much!
https://github.com/Optimal-Control-16-745/lecture-notebooks-2023/blob/main/Lecture%2014/Lecture%2014.pdf