How do you differentiate #f(x)= x/(x^2+1)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Raknos Oct 1, 2017 #{1-x^2}/(1+x^2)^2# Explanation: #={(1+x^2)d/dx (x) - x d/dx (x^2+1)}/(1+x^2)^2# #={1+x^2-x(2x)}/(1+x^2)^2# #={1-x^2}/(1+x^2)^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 1468 views around the world You can reuse this answer Creative Commons License