What is the derivative of #(x^2-1)^3/(x^2+1)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer ali ergin May 22, 2016 #(d y)/(d x)=-2x*(x^2-1)^3/(x^2+1)^2+6x(x^2-1)^2/(x^2+1# Explanation: #d/(d x)(x^2-1)^3/(x^2+1)=?# #d/(d x) (x^2-1)^3/(x^2+1) = (3(x^2-1)^2*2x*(x^2+1)-2x(x^2-1)^3)/(x^2+1)^2# #d/(d x)(x^2-1)^3/(x^2+1)=-2x*(x^2-1)^3/(x^2+1)^2+6x(x^2-1)^2/(x^2+1)# 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 1319 views around the world You can reuse this answer Creative Commons License