How do you find the derivative of #5/((x^2) + x + 1)^2#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Shwetank Mauria Jun 20, 2016 #(dy)/(dx)=(-10(2x+1))/(x^2+x+1)^3# Explanation: Quotient rule states if #f(x)=(g(x))/(h(x))# then #(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2# Hence as #y=5/(x^2+x+1)^2# #(dy)/(dx)=(0xxd/dx(x^2+x+1)^2-d/dx(x^2+x+1)^2xx5)/(x^2+x+1)^4# = #(-2(x^2+x+1)(2x+1)xx5)/(x^2+x+1)^4=(-10(2x+1)(x^2+x+1))/(x^2+x+1)^4# = #(-10(2x+1))/(x^2+x+1)^3# 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 1179 views around the world You can reuse this answer Creative Commons License