개요
- (x+1)/(x-1) 미분
<math>\left( \frac{x+1}{x-1} \right)'</math>
<math>=\left\{ (x+1)(x-1)^{-1} \right\}'</math>[1]
<math>=(x+1)' \cdot (x-1)^{-1} + (x+1) \cdot \left\{ (x-1)^{-1} \right\}'</math>
<math>=\frac{ (x+1)' }{ x-1 } + (x+1) \cdot \left\{ -1 \cdot (x-1)^{-2} \right\}</math>
<math>=\frac{ 1 }{ x-1 } - \frac{ x+1 }{(x-1)^2}</math>[2]
<math>=\frac{x-1-(x+1)}{(x-1)^2}</math>
<math>=\frac{-2}{(x-1)^2}</math>