How do you differentiate #f(x)= e^x/(e^(x^2) +2x )# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Binayaka C. May 14, 2018 #f^'(x) = (e^x( e^(x^2)+2 x)-e^x(2xe ^(x^2)+2))/( e^(x^2)+2 x)^2# Explanation: Quotient rule: #(f/g)^'= (f^' g-f g^')/g^2 # #f(x) = e^x/( e^(x^2)+2 x) # #f^'(x) = (e^x( e^(x^2)+2 x)-e^x(2xe ^(x^2)+2))/( e^(x^2)+2 x)^2# [Ans] 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 1342 views around the world You can reuse this answer Creative Commons License