How do you differentiate #(ln(2x) )/ (cos2x)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Lucio Falabella Jan 11, 2016 #f'(x)=(cos(2x)+2xln(2x)*sin(2x))/(xcos^2(2x))# Explanation: #f(x)=(h(x))/g(x)# with: #h(x)=ln(2x)=>h'(x)=1/(cancel(2)x)*cancel(2)=1/x# #g(x)=cos(2x)=>g'(x)=-sin(2x)*2=-2sin(2x)# Using the Quotient Rule #f'(x)=(h'(x)*g(x)-h(x)*g'(x))/[g(x)]^2# then: #f'(x)=(1/x*cos(2x)-ln(2x)*(-2sin(2x)))/[cos(2x)]^2=# #=(1/x*cos(2x)+2*ln(2x)*sin(2x))/cos^2(2x)=# #(cos(2x)+2xln(2x)*sin(2x))/(xcos^2(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 1648 views around the world You can reuse this answer Creative Commons License