# What is the derivative of y = cot^{-1 }(x)?

To find the derivative of y = cot^{-1 }(x), we will use trigonometric identities.

## Answer: The derivative of y = cot^{-1 }(x) is 1 / (1 + x^{2}).

Here's is the detailed solution.

**Explanation**:

y = cot^{-1}(x),

cot y = x

On differentiating both the sides with respect to 'x', we will get

dy / dx ( - cosec^{2 }y) = 1

We know that d / dx cot x = - cosec^{2 }x

dy / dx = - 1 / ( cosec^{2 }y )

cosec^{2 }x = 1 + cot^{2 }x

dy / dx = - 1 / ( 1 + cot^{2 }y)

By substituting cot y = x , we get dy / dx = - 1 / (1+x^{2 })