What is the derivative of #(-x^2+5)/(x^2+5)^2#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Mauricio M. Mar 8, 2018 #y' = (-2x(x^2 +5)^2 - 2(-x^2 + 5)(x^2 + 5)(2x))/((x^2 +5)^2)^2# Explanation: #y' = (-2x(x^2 +5)^2 - 2(-x^2 + 5)(x^2 + 5)(2x))/((x^2 +5)^2)^2# #y' = (-2x(x^4 + 10x +25) - 4x(-x^4 - cancel(5x^2) +cancel(5x^2) + 25))/((x^2 +5)^4# #y' = (-2x^5 - 20x^2 -50x + 4x^5 - 100x)/((x^2 +5)^4# #y' = (2x^5 - 20x^2 - 150x)/((x^2 +5)^4# 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 1483 views around the world You can reuse this answer Creative Commons License