What is the derivative of tan²x?

Solution:

Differentiation means finding the derivative which is the process of finding the instantaneous rate of change of a function.

According to the rules of differentiation, d/dx(xⁿ) = nx^n-1

According to the chain rule,

dy/dx=f'(g(x)) × g'(x)

Thus,  d/dx(tan²x) = 2 tan x d/dx(tan x) ----------------- (1)

We know that, d/dx (tan x) = sec²x

Substituting in (1) we get,

d/dx(tan²x) = 2 tanx sec²x

Thus, the value when we differentiate tan²x is 2 tanx sec²x.

What is the derivative of tan²x?

Summary:

The value when we differentiate tan²x is 2 tanx sec²x.