How do you differentiate #f(x)=cotx# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Ratnaker Mehta Jul 22, 2016 # f'(x)=-csc^2x#. Explanation: #f(x)=cotx=cosx/sinx# #:. f'(x)=d/dx(cosx/sinx)= (sinx(d/dxcosx)-cosxd/dx(sinx))/(sinx)^2# #={sinx(-sinx)-cosx(cosx)}/sin^2x# #=-(sin^2x+cos^2x)/sin^2x=-1/sin^2x# #-csc^2x#. 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 11542 views around the world You can reuse this answer Creative Commons License