Answer
(a) The derivative of
$$
y=\frac{x+1}{x-1}
$$
is
$$
d y=\frac{\frac{d}{dx}\left(x+1\right)\left(x-1\right)-\frac{d}{dx}\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}=-\frac{2}{\left(x-1\right)^2}d x
$$
(b) When $$ x=2\,\,\,\ \text{and} \,\,\,\,\, d x=0.05
$$,
$$
d y=-\frac{2}{\left(2-1\right)^2} (0.05)=-0.1
$$
Work Step by Step
(a) The derivative of
$$
y=\frac{x+1}{x-1}
$$
is
$$
d y=\frac{\frac{d}{dx}\left(x+1\right)\left(x-1\right)-\frac{d}{dx}\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}=-\frac{2}{\left(x-1\right)^2}d x
$$
(b) When $$ x=2\,\,\,\ \text{and} \,\,\,\,\, d x=0.05
$$,
$$
d y=-\frac{2}{\left(2-1\right)^2} (0.05)=-0.1
$$
