From Wikipedia:
The natural analog of second, third, and higher-order total derivatives is not a linear transformation, is not a function on the tangent bundle, and is not built by repeatedly taking the total derivative.
I think the $n$-th order (total) derivative of a mapping is the derivative of its $n-1$-th order derivative. In other words, derivative can be defined recursively. So I was wondering how to understand that "the natural analog of second, third, and higher-order total derivatives ... is not built by repeatedly taking the total derivative"?
Thanks and regards!