How do you find the derivative of #f(x)= (e^(x)-6)/(3x)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Andrea S. Apr 29, 2017 #d/dx ((e^x-6)/(3x)) = ( e^x(x-1) +6) /(3x^2)# Explanation: Using the quotient rule: #d/dx ((e^x-6)/(3x)) = (3x d/dx(e^x-6) - (e^x-6) d/dx (3x))/(3x)^2# #d/dx ((e^x-6)/(3x)) = (3x e^x - 3(e^x-6) )/(9x^2)# #d/dx ((e^x-6)/(3x)) = ( e^x(x-1) +6) /(3x^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 1316 views around the world You can reuse this answer Creative Commons License