I need short, sweet, simple proofs for all the derivatives of , , and concurrently so as to avoid a "chicken or the egg" situation in which 1 proof relies on one of the other 3 results.

Note:

Caution: Do not commit circular reasoning like what I have encountered.

Anyone who can do so is likely to benefit most of us who are learning derivatives.

"Proof is what sets mathematics apart from every other science." ----Prove It, MHF Contributor

Thank You.