[cschmidt]

I do derivations all the time. I just do a series of algebraic transformations, starting from what I have, and getting to what I need. Some might say that I'm doing a proof. But I never use proof by contradiction, contrapositive, induction, or proper proof techniques.

[j2kun]

Doing a derivation like that is sometimes called a proof by "chaining if and only ifs", though that's far from a standard name taught to students. It's basic, but most certainly a required method of proof to come up with convenient formulas.