How do you differentiate #f(x) = (-11x) / (sin(x)+cos(x))#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Lucy Apr 29, 2018 #f'(x)=((11sinx)(x+1)+(11cosx)(1-x))/(sinx+cosx)^2# Explanation: #f(x)=(-11x)/(sinx+cosx)# #f'(x)=((cosx-sinx)(-11x)-(sinx+cosx)times(-11))/(sinx+cosx)^2# #f'(x)=(-11xcosx+11xsinx+11sinx+11cosx)/(sinx+cosx)^2# #f'(x)=((11sinx)(x+1)+(11cosx)(1-x))/(sinx+cosx)^2# Remember: IF #f(x)=u/v# THEN #f'(x)=(v'u-vu')/v^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 1763 views around the world You can reuse this answer Creative Commons License