I have to find the $n^{\text{th}}$ derivative of the following function
$$y= \frac{x+2}{\sqrt[3]{1-x}}$$
I tried taking the derivative for a couple of times to find some patterns but it didn't help.
I feel like I have to use some formulas for common function's $n^{\text{th}}$ derivative, but in my function-as you can see- there are 2 types of functions so I don't know what i should do. Also I don't know any series yet, I don't know if that was necessary, just in case. Could you please help me?
Thanks.
Best Answer
hint
Use the Leibnitz formula, which gives the $n^{\text{th}} $ derivative of a product : $$(f.g)^{(n)} = \sum_{k=0}^n \binom {n}{k} f^{(k)}g^{(n-k)}$$
with
$$f(x)=x+2, \;\; f''=f^{(3)}=...=0$$ and $$g(x)=(1-x)^{-\frac 13}$$