notation for multiple gradient?

Question

Suppose I have $f(x_1,x_2,\cdots,x_n)$ where $x_1,\cdots,x_n$ are vectors with the same length. I write $\nabla_{x_n}\nabla_{x_{n-1}}\cdots \nabla_{x_1}f(x_1,x_2,\cdots,x_n)$. Is there any simple notation to represent $\nabla_{x_n}\nabla_{x_{n-1}}\cdots \nabla_{x_1}$?