I'm not sure what you mean by "derive".

For a more mathematical and geometric description of the super Poincaré group you could check out lecture notes by

- Dan Freed, [Lectures on field theory and supersymmetry][1], see Lecture 6, or
- Kevin Costello, e.g. [arXiv:1401.2676][2], see Section 1.1.

[1]: https://www.ma.utexas.edu/users/dafr/pcmi.pdf
[2]: https://arxiv.org/abs/1401.2676