Quotient rule of derivatives Quotient rule of derivative is: $(\frac{f}{g})^{\prime}$ = $(\frac{f^{\prime}g - g^{\prime}f}{g^2})$ but when I compute a deriative of $\frac{1}{(1-x)}$ , it gives  $\frac{1}{(1-x)^2}$ which is right but taking second derivative of this gives me $\frac{2}{(1-x)^4}$ but the right answer is $\frac{2}{(1-x)^3}$. Where do I make a mistake?

You get this because you can cancel out one $(1-x)$ in the denominator.
$\Big(\frac{1}{(1-x)^2}\Big)'=\frac{0*((1-x)^2)'-1*((1-x)^2)'}{((1-x)^2)^2}=\frac{2(1-x)}{(1-x)^4}=\frac{2}{(1-x)^3}$.
If you just follow the formula you had carefully, with $f=1$ and $g=(1-x)^2$, this is what you get.
