How do you find the derivative of #(x^2-4)/(x-1)#?

1 Answer
Mar 12, 2017

#d/(dx) ((x^2-4)/(x-1)) = 1+3/(x-1)^2#

Explanation:

I would simplify the expression first, then use the power rule...

#d/(dx) ((x^2-4)/(x-1)) = d/(dx) ((x^2-x+x-1-3)/(x-1))#

#color(white)(d/(dx) ((x^2-4)/(x-1))) = d/(dx) (((x+1)(x-1)-3)/(x-1))#

#color(white)(d/(dx) ((x^2-4)/(x-1))) = d/(dx) ((x+1)-3/(x-1))#

#color(white)(d/(dx) ((x^2-4)/(x-1))) = d/(dx) (x+1-3(x-1)^(-1))#

#color(white)(d/(dx) ((x^2-4)/(x-1))) = 1+0+3(x-1)^(-2)#

#color(white)(d/(dx) ((x^2-4)/(x-1))) = 1+3/(x-1)^2#

#color(white)()#
Note: I did use the chain rule quietly above too, when differentiating:

#(x-1)^(-1)#

to get:

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