### The derivative of y = tan^{2}x is dy/dx = 2 sec^{2}x 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.

**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 = tan^{2}x

dy/dx = (2 tan x) × (dy/dx(tan x))

= 2 tanx sec^{2}x