Load the Physics package and set a prefix to identify anticommutative variables (see Setup for more information).
Consider a commutative function depending on commutative and anticommutative variables, and one higher order derivative of it.
Note in the above that the commutative differentiation variables are collected as a group to be applied first, then the anticommutative ones.
Physics:-diff(Physics:-diff(Physics:-diff(diff(diff(diff(f(x,y,z,theta[1],theta[2],theta[3]),x),y),z),theta[1]),theta[2]),theta[3])
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Rewrite this expression in D notation, then convert back to diff notation.