Common Derivatives:
* perceive: to become aware of through the senses.
* perfect: completely finished or without any flaws.
* perform: to carry out an action or task.
* permanent: lasting or intended to last forever.
* permission: consent or authorization.
* persuade: to convince someone to do something.
* persevere: to continue in spite of difficulties.
* perspective: a particular attitude toward or way of regarding something.
* pertinent: relevant to the matter at hand.
* perturb: to make someone anxious or upset.
* pervade: to spread throughout.
* perverse: contrary to what is expected or accepted.
* peril: serious and immediate danger.
Less Common Derivatives:
* perennial: lasting for a long time or recurring year after year.
* perjury: the crime of deliberately lying in a court of law.
* perceptible: able to be perceived.
* percussion: the act of striking something.
* perambulate: to walk around an area.
* percolate: to filter through a porous substance.
These are just a few examples, and there are many other words in English that are derived from the Latin root "per".
It's important to note that the meaning of the derivative can sometimes be slightly different from the original meaning of the root word. However, the basic idea of "through", "by", or "thoroughly" is usually present in some form.