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?

$\require{cancel}$
$\Big(\dfrac{1}{(1-z)^2}\Big)'=\dfrac{0\times(1-z)^2-2(-1)(1-z)\times1}{(1-z)^4}=\dfrac{2(1-z)}{(1-z)^4}=\dfrac{2‎‏\cancel{(1-z)}}{(1-z)^\cancel{4}}=\dfrac{2}{(1-z)^3}$
