noun
: a mathematical rule concerning the differentiation of a function of a function (as f[u(x)] ) by which under suitable conditions of continuity and differentiability one function is differentiated with respect to the second considered as an independent variable and then the second function is differentiated with respect to its independent variable
if v=u 2 and u =3 x 2 +2 the derivative of v by the chain rule is 2 u (6 x ) or 12 x (3 x 2 +2)