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 2016 views around the world You can reuse this answer Creative Commons License