How do you differentiate #f(x)= e^x/(e^(3x) -5x)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Ratnaker Mehta Jun 23, 2016 #f'(x)={e^x(5-5x-2e^(3x))}/(e^(3x)-5x)^2.# Explanation: The Quotient Rule : #(u/v)'=(vu'-uv')/v^2.# #:. f'(x)={(e^(3x)-5x)(e^x)'-e^x(e^(3x)-5x)'}/(e^(3x)-5x)^2={(e^(3x)-5x)e^x-e^x(3*e^(3x)-5)}/(e^(3x)-5x)^2=[e^x{e^(3x)-5x-3e^(3x)+5}]/(e^(3x)-5x)^2={e^x(5-5x-2e^(3x))}/(e^(3x)-5x)^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 1493 views around the world You can reuse this answer Creative Commons License