# 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.

## Answer: The derivative of f (x) = tan^{-1} (x) is 1/ (1 + x^{2 })

Here's the solution to arc tan x.

**Explanation:**

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

sec^{2 }y.dy/dx = 1

⇒ dy/dx = 1 / sec^{2 }y

⇒ dy/dx = 1 / (1+ tan^{2 }y), ∵ 1+ tan^{2 }y = sec^{2 }y

Since tan y = x, we get

dy/dx = 1 / (1 + x^{2}),

⇒ d/dx (tan^{-1} (x) = 1 / (1 + x^{2})