right and left derivatives of a cfg from parse tree? i just want to double check with what i concluded from this parse trees.


       A
      / \
     /   \
    B      C
   / \    / \
  0   D  D   E
         |   |
         0   1



from the above tree i get right derivation to be 


  A -> C
  
  C -> D|E
  
  E -> 1
  
  D -> 0


and the left derivation as 


  A -> B
  
  B -> 0|D
  
  D -> 0


i just want someone to proof check for me. and tell me if am wrong somewhere. Thanks!
What you wrote are not derivations, they are grammars.

The leftmost derivation in your case is $A \to BC \to 0DC \to 0DDE \to 0D0E \to 0D01$. I'll leave you to figure out the rightmost derivation.