How do you use the quotient rule to differentiate #(2x+1)/(x^2-1)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Tony B Jan 20, 2016 #(dy)/(dx)= (-2(x^2+x+1))/(x^2-1)^2# Explanation: Standard form: # (d)/dx (u/v)=(dy)/(dx)= (v (du)/(dx) - u(dv)/(dx))/v^2# Given:#color(white)(..) y=(2x+1)/(x^2-1)# #(dy)/(dx)= ((x^2-1)2-(2x+1)2x)/(x^2-1)^2# #(dy)/(dx)= (2x^2-2-4x^2-2x)/(x^2-1)^2# #(dy)/(dx)= (-2x^2-2x-2)/(x^2-1)^2# But #-2x^2-2x-2= -2(x^2+x+1)# #(dy)/(dx)= (-2(x^2+x+1))/(x^2-1)^2# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 10989 views around the world You can reuse this answer Creative Commons License