What is the derivative of cot⁻¹(x)?

The derivative of the inverse cotangent function, denoted as cot⁻¹(x), can be derived using calculus. The formula for the derivative is:

Derivative Formula

If y = cot⁻¹(x), then the derivative with respect to x is given by:

Mathematical Expression

dy/dx = -1 / (1 + x²)

Understanding the Components

• Negative Sign: Indicates that the function is decreasing.
• 1 + x²: This expression is always positive, ensuring the derivative is defined for all real x.

Applications

This derivative is useful in various fields, including physics and engineering, where inverse trigonometric functions often appear in calculations involving angles and rates of change.