How do you differentiate #f(x)=x/(1-sinx)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Bdub Apr 8, 2016 #f'(x)=(1-sinx+xcosx)/(1-sinx)^2# Explanation: let #f=x# and #g=1-sinx# #f'=1,g'=-cosx# Quotient Rule: #f'(x)=(gf'-fg')/g^2# #f'(x)=((1-sinx)(1)-(x)(-cosx))/(1-sinx)^2# #f'(x)=(1-sinx+xcosx)/(1-sinx)^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 1447 views around the world You can reuse this answer Creative Commons License