What is the derivative of #(2ln(x+3))/x^2#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Shubh Apr 1, 2018 answer = #"-2(x+6)"/x^3# Explanation: #d/dx(u/v)="u'v-v'u"/v^2# similarly, #d/dx((2(x+3))/x^2)=d/dx((2x+6)/x^2)# =#((x^2)d/dx(2x+6)-(2x+6)d/dx(x^2))/(x^2)^2# =#((x^2)(2)-(2x+6)(2x))/x^4# =#(2x^2-4x^2-12x)/x^4# #(-2x^2-12x)/x^4# #(-2x(x+6))/x^4=(-2(x+6))/x^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 1842 views around the world You can reuse this answer Creative Commons License