Solution
= Solution
Differentiate the product $4(x-1)^{-2}(x+1)^{-1}$ using the <product rule> and <chain rule>:
$$
f'(x)=-8(x-1)^{-3}(x+1)^{-1}-4(x-1)^{-2}(x+1)^{-2}.
$$
Combining terms over a common denominator gives
$$
\boxed{f'(x)=-\frac{4(3x+1)}{(x-1)^3(x+1)^2},\qquad x\ne\pm1.}
$$