What is the derivative of #5/(x^2+1)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer salamat Jan 23, 2017 #(-10x)/(x^2+1)^2# Explanation: Let #u=5# and #v=x^2+1# #u' = 0 and v'=2x# Let say #y=5/(x^2+1) =u/v# #y'=(vu'-uv')/v^2# #y'=((x^2+1)*0-5(2x))/(x^2+1)^2# #y'=(-5(2x))/(x^2+1)^2# #y'=(-10x)/(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 3571 views around the world You can reuse this answer Creative Commons License