How do you differentiate #f(x)=secx# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Praveer Sharan Nov 29, 2017 #f'(x) = secxtanx# Explanation: #f(x) = sec x# #= 1/cos x# #f'(x) = ([1]' * cos x - [cos x]' * 1)/cos^2x# #=(0 * cos x - (-sin x) * 1)/cos^2x# #=(0 + sin x)/cos^2x# #=sinx/cos^2x# #=sinx/cosx * 1/cosx# #=1/cosx * sinx/cosx# #=secx*tanx# #=secxtanx# Hope that helps. 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 7873 views around the world You can reuse this answer Creative Commons License