How do you differentiate #f(x) = (e^(4-x))/(e^(1-x)-1)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Sasha P. Apr 20, 2017 #f'(x) = e^(4-x) / (e^(1-x)-1)^2# Explanation: #f(x)=u/v, f'(x)=(u'v-v'u)/v^2# So, we need #u'# and #v'#: #u' = (e^(4-x))' = e^(4-x) * (4-x)' = -e^(4-x)# #v' = (e^(1-x) - 1)' = e^(1-x) * (1-x)' = -e^(1-x)# #f'(x) = (-e^(4-x) * (e^(1-x) - 1) + e^(1-x) * e^(4-x)) / (e^(1-x)-1)^2# #f'(x) = (-e^(5-2x) + e^(4-x) + e^(5-2x)) / (e^(1-x)-1)^2# #f'(x) = e^(4-x) / (e^(1-x)-1)^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 1393 views around the world You can reuse this answer Creative Commons License