How do you differentiate #f(x)= (x+5)/ (x- 7 )# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Lucio Falabella Jan 7, 2016 #f'(x)=-12/(x-7)^2# Explanation: Given: #f(x)=(N(x))/(D(x))# #f'(x)=(N'(x)*D(x)-D'(x)*N(x))/((D(x))^2)# Then: #f'(x)=(1*(x-7)-1*(x+5))/(x-7)^2=(cancel(x)-7cancel(-x)-5)/(x-7)^2=# #=-12/(x-7)^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 1327 views around the world You can reuse this answer Creative Commons License