Let R be ring, and d:R R is aditif mapping then

d is called derivation if

d(ab)=d(a)b+ad(b) a,b R

d is called Jordan derivation if

d(a^2)=d(a)a+ad(a) a R

Obviously any derivation is Jordan derivation.

But the converse is not true. (is there any example to show this statement?)