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?

Let's derive
$$\left({1\over (1-x)^2}\right)^{'}={(1)'\cdot (1-x)^2-1\cdot\left((1-x)^2\right)^{'}\over (1-x)^4}$$
Now $(1)'=0$, $\left((1-x)^2\right)^{'}=-2(1-x)$ and so the derivative rewrites as
$$\left({1\over (1-x)^2}\right)^{'}={2(1-x)\over (1-x)^4}={2\over (1-x)^3}$$
