The derivative of y = tan2x is dy/dx = 2 sec2x tan x
The derivative of any function y = f(x) of a variable x is a measure of the rate at which the value y changes with respect to the change of x.
Let us proceed for this problem step by step.
We can proceed by using chain rule.
It states that for any function, y = f(g(x))
=> d/dx ( f(g(x) ) = f' (g(x)) · g' (x)
Given y = tan2x
dy/dx = (2 tan x) × (dy/dx(tan x))
= 2 tanx sec2x