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Answer 1 · 2018-01-19T02:58:14

#y'=1/(x+1)^2#

#y'=d/dx(f(x)/g(x))=(d/dx[f(x)]g(x)-d/dx[g(x)]f(x))/(g(x))^2#

Given: #(2x+1)/(x+1)#

Let

#f(x)=2x+1=>d/dx[f(x)]=2#

#g(x)=x+1=>d/dx[g(x)]=1#

Substituting into the quotient rule

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

Simplifying:

#y'=((2x+2)-(2x+1))/(x+1)^2=((cancel(2x)+2)-(cancel(2x)+1))/(x+1)^2=1/(x+1)^2#