How do you differentiate #f(x)= e^x/(e^(-x) -x )# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Sonnhard May 28, 2018 #f'(x)=(2-x*e^x+e^x)/(e^(-x)-x)^2# Explanation: Using the Quotient rule we get #f'(x)=(e^x(e^(-x)-x)-e^x(-e^(-x)-1))/(e^(-x)-x)^2# Expanding and collect equal Terms we get the result above. 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 1352 views around the world You can reuse this answer Creative Commons License