Studying Continuum Mechanics with Capaldi's book [1, p.27], he states that the gradient can each be expressed in terms of a vector differential operator named the Del operator, which is defined in Cartesian coordinates as either a right-differential operator, $\overrightarrow{\nabla}$,or left-differential operator,$\overleftarrow{\nabla}$. The direction of the arrow signifies the direction in which the operator acts, according to the book.
Does anybody have a clue on what do they mean with the "direction which the operator acts"?
[1] Capaldi, Franco. 2012. Continuum Mechanics : Constitutive Modeling of Structural and Biological Materials. Cambridge, MA: Cambridge University Press.
Normally an operator is placed to the left of what it's acting on: $\nabla\phi.$
But sometimes it is however useful to have it placed to the right of what it's acting on. Then an arrow is used to mark in what direction it acts: $\phi\overleftarrow{\nabla}$.