What is the derivative of #tan(2x)#? Calculus Differentiating Trigonometric Functions Special Limits Involving sin(x), x, and tan(x) 1 Answer sjc Oct 26, 2016 #(dy)/(dx)=2sec^2(2x)# Explanation: #y=tan(2x)# # u=2x=>(du)/dx=2# #y=tanu=>(dy)/(du)=sec^2u# the chain rule: #(dy)/(dx)=(dy)/(du)xx(du)/(dx)# #:.(dy)/(dx)=(sec^2u)xx2# #(dy)/(dx)=2sec^2u=2sec^2(2x)# 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) #? How do you differentiate #f(x)=sinx/x#? How do you differentiate #f(x)=sinx/(1-cosx)#? How do you differentiate #f(x)=(x+2)/cosx#? See all questions in Special Limits Involving sin(x), x, and tan(x) Impact of this question 7874 views around the world You can reuse this answer Creative Commons License