Differentiate cot⁻¹(x) with respect to x?

Given: The problem asks for the derivative of cot^-1(x) with respect to x.

Concept Used: The derivative of the inverse cotangent function cot^-1(x) is given by:

d/dx [cot^-1(x)] = -1 / (1 + x²).

This formula arises from the differentiation rules of inverse trigonometric functions.

Calculation: Start with the formula:   d/dx [cot^-1(x)] = -1 / (1 + x²)

Compare this with the options provided:  

Option 2 matches the formula: -1 / (1 + x²).

⇒ Therefore, the correct answer is Option 2.