What is the $n^{th}$ term derivative of $f(x) = (x^2-x-1)(\ln(1-x))$? I have the first three terms but am struggling with finding the $n^{th}$ term derivative of the function. Here is my work:
$$\\$$
$$f(x) = (x^2-x-1)(\ln(1-x)) $$
$$f'(x) = (2x-1)(\ln(1-x))-\left(\dfrac{x^2-x-1}{1-x}\right)$$
$$f''(x) = \dfrac{3x^2-5x+2(x-1)^2 \ln(1-x)+3}{(1-x)^2}$$
$$f'''(x) = \dfrac{2x^2-5x+1}{(x-1)^3}$$
$$f^{(n)}(x) = \ ?$$

Use the following.
$$f'''(x)=\frac{2x^2-5x+1}{(x-1)^3}=\frac{2x^2-4x+2-x+1-2}{(x-1)^3}=\frac{2}{x-1}-\frac{1}{(x-1)^2}-\frac{2}{(x-1)^3}.$$
Can you end it now?
