How do you differentiate #f(x) = (x^2-4x)/(xcotx+1)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Καδήρ Κ. Jul 21, 2017 #(df)/dx=((2x-4)(xcotx+1)+(x/sin^2theta-cotx)(x^2-4x))/(xcotx+1)^2# Explanation: #(df)/dx=((d(x^2-4x))/dx(xcotx+1)-(d(xcotx+1))/dx(x^2-4x))/(xcotx+1)^2=# #((2x-4)(xcotx+1)-(-x/sin^2theta+cotx)(x^2-4x))/(xcotx+1)^2=# #((2x-4)(xcotx+1)+(x/sin^2theta-cotx)(x^2-4x))/(xcotx+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 1486 views around the world You can reuse this answer Creative Commons License