How do you use the quotient rule to differentiate #x^6/(x-6)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Bdub Apr 14, 2016 #f'(x)=(5x^6-36x^5)/(x-6)^2# Explanation: Let #f=x^6 and g=x-6# Then#f'=6x^5 and g'=1# Quotient Rule: #f'(x)=(gf'-fg')/g^2# #f'(x)=((x-6)(6x^5)-(x^6))/(x-6)^2# #=(6x^6-36x^5-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 1442 views around the world You can reuse this answer Creative Commons License