How do you differentiate #f(x) = (x^2-4x)/(x+1)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Topscooter Jan 17, 2016 #f'(x) = ((2x - 4)(x+1) - x^2 + 4x)/(x+1)^2# Explanation: Let #f(x) = (u(x))/(v(x))# where #u(x) = x^2 - 4x# and #v(x) = x+1#. By the quotient rule, #f'(x) = (u'(x)v(x) - u(x)v'(x))/(v(x))^2#. Here, #u'(x) = 2x - 4# and #v'(x) = 1#. So #f'(x) = ((2x - 4)(x+1) - x^2 + 4x)/(x+1)^2# by direct use of the quotient rule. 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 1709 views around the world You can reuse this answer Creative Commons License