Both classical methods have problems with calculating higher derivatives, where the complexity and errors increase.

Higher order moments and cumulants are obtained by higher derivatives.

The next terms are all zero as they contain higher derivatives.

The local structure is determined by higher derivatives of .

It is assumed below, in addition, that the Lagrangian depends on only the field value and its first derivative but not the higher derivatives.

They involve higher derivatives and are therefore somewhat less easy to apply than the Alfrey approximation.

If the coefficient at the highest derivative is constant, then all solutions of such equations are entire functions.

The above arithmetic can be generalized, in the natural way, to calculate parts of the second order and higher derivatives.

Nevertheless, higher derivatives have important applications to analysis of local extrema of a function at its critical points.

Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk.