What is the derivative of tan2x?
Differentiation means finding the derivative which is the process of finding the instantaneous rate of change of a function.
Answer: The value when we differentiate tan2x is 2 tanx sec2x.
Let's understand the steps to solve the given question.
According to the rules of differentiation, d/dx(xn) = nxn-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.