ProofWiki:Sandbox

Question, is there such a theorem as the following?

If p(x) = q(x) then p'(x) = q'(x), provided that p and q are differentiable.

I can't even find the name of such a property, let alone the proof.

Please post the answer on my talk page http://tinyurl.com/43waowe as I'm not watching the sandbox. --GFauxPas 20:15, 6 October 2011 (CDT)