# calculation and analysis: evaluate the higher order derivative at some point under some assumptions

I need to evaluate the $$k ^ { rm th}$$ derivative of order

``````re[w
``````

which is really equal to

``````Sum[Binomial[k, j] re[w
``````

to `t = 0`. I get that `w[0]== 0` Y `w & # 39;[0]== 0`.

I'm trying

``````Evaluate[RE[D[RE[D[w
``````

and so

``````FullSimplify[3w&#39;[3w'[3w'[3w'[0]w & # 39; & # 39;[0] + w[0]w & # 39; & # 39; & # 39;[0], Assumptions -> w[0] == 0 && w & # 39;[0] == 0]
``````

but this works only for fixed `k`.

Is there any way to do the evaluation in `t = 0` under the assumptions `w[0]== 0` Y `w & # 39;[0]== 0` for arbitrary `k` and also take into account the value of evaluations up to `k-1` order? Any help is appreciated. Thank you.