# What is the derivative of tan-1(x)?

#### Understand the Problem

The question is asking for the derivative of the inverse tangent function, denoted as tan^(-1)(x) or arctan(x). The derivative of this function is a common calculus problem, where we will use the formula for the derivative of arctan(x).

The derivative of the inverse tangent function is $$\frac{dy}{dx} = \frac{1}{1 + x^2}$$

The derivative of the inverse tangent function is $$\frac{dy}{dx} = \frac{1}{1 + x^2}$$

#### Steps to Solve

1. Identify the Function and Formula

We start with the function we need to differentiate, which is $y = \tan^{-1}(x)$ or $y = \arctan(x)$.

1. Use the Derivative Formula

The standard formula for the derivative of arctan(x) is: $$\frac{dy}{dx} = \frac{1}{1 + x^2}$$

1. Compute the Derivative

Now we apply the derivative formula directly: For $y = \tan^{-1}(x)$, we substitute $x$ into the formula: $$\frac{dy}{dx} = \frac{1}{1 + x^2}$$

The derivative of the inverse tangent function is $$\frac{dy}{dx} = \frac{1}{1 + x^2}$$