How do you find the derivative for #f(x) =x^6/(x-6)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Trevor Ryan. Oct 18, 2015 #d/dx(x^6/(x-6))=(5x^6-36x^5)/(x-6)^2# Explanation: Using the quotient rule : #d/dx[f(x)/g(x)]=(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2#, we get: #d/dx(x^6/(x-6))=(6x^5(x-6)-x^6)/(x-6)^2# #=(5x^6-36x^5)/(x-6)^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 1227 views around the world You can reuse this answer Creative Commons License