What is the derivative of f (x) = tan-1 (x)?
In mathematics, the inverse trigonometric function is also known as 'arc functions'. To find the derivative of f (x) = tan-1 (x) we will use inverse identity.
Here's the solution to arc tan x.
f (x) = tan-1 (x)
Let y = tan-1 (x)
⇒ tan y = x
On differentiating both the sides with respect to 'x', we will get
sec2 y.dy/dx = 1
⇒ dy/dx = 1 / sec2 y
⇒ dy/dx = 1 / (1+ tan2 y), ∵ 1+ tan2 y = sec2 y
Since tan y = x, we get
dy/dx = 1 / (1 + x2),
⇒ d/dx (tan-1 (x) = 1 / (1 + x2)