Question #da685

1 Answer
Andrea S.
Feb 3, 2018

#d/dx (x/(x-1)) = -1/(x-1)^2#

Explanation:

#d/dx (x/(x-1)) = lim_(h->0) 1/h( (x+h)/(x+h-1) - x/(x-1))#

#d/dx (x/(x-1)) = lim_(h->0) 1/h(( (x+h)(x-1) -x(x+h-1))/((x+h-1)(x-1)))#

#d/dx (x/(x-1)) = lim_(h->0) 1/h( (color(red)(x^2)+ color(blue)(hx) - color(green)(x) - h - color(red)(x^2)- color(blue)(hx) + color(green)(x))/((x+h-1)(x-1)))#

#d/dx (x/(x-1)) = lim_(h->0) 1/cancel(h)( -cancel(h))/((x+h-1)(x-1))#

#d/dx (x/(x-1)) = lim_(h->0) -1/((x+h-1)(x-1))#

#d/dx (x/(x-1)) = -1/(x-1)^2#

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