(x+1)/(x-1) 미분

1 개요

[math]\displaystyle{ \left( \frac{x+1}{x-1} \right)' }[/math]

[math]\displaystyle{ =\left\{ (x+1)(x-1)^{-1} \right\}' }[/math]

[math]\displaystyle{ =(x+1)' \cdot (x-1)^{-1} + (x+1) \cdot \left\{ (x-1)^{-1} \right\}' }[/math]

[math]\displaystyle{ =\frac{ (x+1)' }{ x-1 } + (x+1) \cdot \left( (x-1)^{-1} \right)' }[/math]

[math]\displaystyle{ =\frac{ 1 }{ x-1 } + (x+1) \cdot \left( \frac{-1}{(x-1)^2} \right) }[/math]