How do you differentiate #f(x)= e^x/(x-3 )# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Andrea S. Jan 25, 2017 #d/(dx) (e^x/(x-3)) = (e^x(x-4))/(x-3)^2# Explanation: The quotient rule states that: #d/(dx)( f(x)/g(x) )= (f'(x)g(x) -f(x)g'(x))/(g(x))^2# For #f(x) = e^x# and #g(x) = x-3# we have: #d/(dx) (e^x/(x-3)) = (e^x(x-3) - e^x)/(x-3)^2 = (e^x(x-4))/(x-3)^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 1510 views around the world You can reuse this answer Creative Commons License