# What is the derivative of tan^{-1}x?

We will be finding the derivative of tan^{-1 }by using the concept of derivatives and inverse trigonometric functions.

## Answer: The derivative of tan^{-1}x is [1] / [1 + x^{2}].

Let's get the solution step by step.

**Explanation**:

Given: f(x) = tan^{-1}x

Let y = tan^{-1}x

Thus, tan y = x

⇒ x = tan y ---------------- (1)

Differentiate both sides w.r.t.x

(dx/dx) =d(tan y)/dx

⇒ 1 = [d(tan y)/dx] × [dy/dy]

⇒ 1 = [d(tan y)/dy] × [dy/dx] [Multiplying and dividing by 'dy']

⇒ 1 = [sec^{2}y] dy/dx

⇒ 1 = [1 + tan^{2}y] dy/dx [Using trigonometric identities, sec^{2}y = 1 + tan^{2}y]

dy/dx = [1] / [1 + tan^{2}y]

Substituting tan y = x [From (1)]

dy/dx = [1] / [1 + x^{2}]

We can calculate the derivatives by using Cuemath's Derivatives Calculator.