How do you differentiate #f(x)= e^x/(e^(-x) -2)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Bio Jan 14, 2016 #f'(x) = 2frac{1-e^x}{(e^{-x}-2)^2} # Explanation: #f'(x) = frac{d}{dx}(frac{e^x}{e^{-x}-2})# #= frac{(e^{-x}-2)frac{d}{dx}(e^x)-e^xfrac{d}{dx}(e^{-x}-2)}{(e^{-x}-2)^2} # #= frac{(e^{-x}-2)e^x-e^x(-e^{-x})}{(e^{-x}-2)^2} # #= frac{1-2e^x+1}{(e^{-x}-2)^2} # #= 2frac{1-e^x}{(e^{-x}-2)^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 1121 views around the world You can reuse this answer Creative Commons License