How do you differentiate #f(x)= (1 - sin^2x)/(x-cosx) # using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Sonnhard Jun 11, 2018 #f'(x)=(cos(x)(cos(x)(sin(x)-1)-2xsin(x)))/(x-cos(x))^2# Explanation: We have #f'(x)=(2cos(x)(-sin(x))(x-cos(x)-cos^2(x)(1+sin(x))))/(x-cos(x))^2# I have used that #f(x)=cos^2(x)/(x-cos(x))# since #1-sin^2(x)=cos^2(x)# 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 1533 views around the world You can reuse this answer Creative Commons License