What is the derivative of #y= (x^2 + 2x + 5) / (x + 1)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Antoine Apr 17, 2015 #y = (x^2 + 2x + 5)/(x + 1)# #=> (dy)/(dx) = ((x + 1)(2x + 2) - (x ^2 + 2x + 5)(1))/(x + 1)^2# #= (2x^2 + 4x + 2 - x^2 - 2x - 5)/(x + 1)^2 = (x^2 + 2x - 3)/(x + 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 1139 views around the world You can reuse this answer Creative Commons License