Y' =(х÷(х-1)²)' найти производную

[latex]y`= (\frac{x}{(x-1) ^{2} })`=[ (\frac{u}{v})`= \frac{u`\cdot v- u\cdot v`}{v ^{2} }]= \frac{x`(x-1) ^{2}-x\cdot((x-1) ^{2})` }{((x-1) ^{2})^{2} }= \\ =\frac{1\cdot (x-1) ^{2}-x\cdot2(x-1)\cdot (x-1)` }{(x-1) ^{4} } =\frac{(x-1)(x-1-2x) }{(x-1) ^{4} } = -\frac{(x+1) }{(x-1) ^{3} } [/latex]