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'[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.