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What is the derivative of #y=(x^2 - 1) /( x+1)#?

1 Answer

Jan 26, 2016

#2/(x^2-1)#

Explanation:

Use the quotient rule, which states that if #f(x) = g(x)/(h(x))# then
#f'(x) = (h(x)g'(x) - h'(x)g(x))/(g^2(x))#

#g(x) = (x^2-1)# so #g'(x) = 2x#
#h(x) = (x+1)# so #h'(x) = 1#

#f'(x) = ((x+1)(2x) - 1*(x+1))/(x^2-1)^2#
#=(2x^2+x-1-x-1)/(x^2-1)^2#
#=(2x^2-2)/(x^2-1)^2#
#=(2(x^2-1))/(x^2-1)^2#
#=2/(x^2-1)#

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