How do you use the quotient rule to find the derivative of #y=x/(x-1)^2# ?

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Answer 1 · 2014-09-21T10:44:45

By Quotient Rule,

#y'={1 cdot (x-1)^2-x cdot2(x-1)}/{[(x-1)^2]^2}#

by factoring out #(x-1)# from the numerator,

#={(x-1)(x-1-2x)}/{(x-1)^4}#

by cancelling out #(x-1)#,

#={-x-1}/{(x-1)^3}#

by factoring out #-1# from the numerator,

#=-{x+1}/{(x-1)^3}#