How do you differentiate #f(x)=tanx/(cosx-4)#? Calculus Differentiating Trigonometric Functions Special Limits Involving sin(x), x, and tan(x) 1 Answer Monzur R. Feb 12, 2017 #f'(x)=(sec^2x(cosx-4)+sinxtanx)/(cosx-4)^2# Explanation: Using the quotient rule, we get: #f'(x)=(sec^2x(cosx-4)+sinxtanx)/(cosx-4)^2# Answer link Related questions What are Special Limits Involving #y=sin(x)#? How do you find the limit #lim_(x->0)sin(x)/x# ? How do you find the limit #lim_(x->0)tan(x)/x# ? What is the derivative of #tanx^3#? What is the derivative of #tanx/x#? How do you differentiate # g(x) =sin^2(x/6) #? How do you differentiate # g(x) =(1+cosx)/(1-cosx) #? What is the derivative of #tan(2x)#? How do you differentiate #f(x)=sinx/x#? How do you differentiate #f(x)=sinx/(1-cosx)#? See all questions in Special Limits Involving sin(x), x, and tan(x) Impact of this question 4366 views around the world You can reuse this answer Creative Commons License