How do you find the derivative of y = tan²x?

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. 

Answer: The derivative of y = tan²x is dy/dx = 2 sec²x tan x

Let us proceed for this problem step by step.

Explanation:

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