Question

If $y=\frac{x+1}{x-1}$ , then what is $\frac{dy}{dx}$ equal to ?

• A. $\frac{-2}{x-1}$
• B. $\frac{-2}{(x-1{)}^2}$
• C. $\frac{2}{(x-1{)}^2}$
• D. $\frac{2}{(x-1)}$

Answer 1

The correct option is B $\frac{-2}{(x-1{)}^2}$

For fraction derivative, $\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{vdu-udv}{v^2}$

Given $y=\frac{x+1}{x-1}$

$\Rightarrow \frac{dy}{dx}=\frac{(x-1)-(x+1)}{{(x-1)}^2}=\frac{-2}{{(x-1)}^2}$