The common high-order derivative formulas are Leibniz formula (UV) (n) = u (n) v+nu (n-1) v'+n (n-1)/2! u(n-2)v"+n(n- 1)...(n-k+ 1)u(n-k)v(k)+...+uv(n)； Any derivative of e(x) is e(x), that is, the n power of e(x) =e(x).

Calculation of arbitrary derivative;

For the calculation of any n-order derivative, because n is not a definite value, it is naturally impossible to calculate it by step-by-step derivation. In addition, it is impossible to calculate the fixed-order derivative step by step when its order is high.

The so-called calculation of n-order derivative is actually trying to find the expression of derivative function with n as parameter. There is no general method to find the parameter expression of n-order derivative. The most common method is to find several derivatives according to the derivative calculation method, and then try to find out the regularity between them, and then deduce the parameter relationship of n.