We shall prove formula for derivative of cotangent function using by definition or first principle method.

Let us suppose that the function of the form .

First we take the increment or small change in the function.

Putting the value of function $y = \cot x$ in the above equation, we get

Using formula from trigonometry, we have

Using this formula in equation (i), we get

Dividing both sides by , we get

Taking limit of both sides as , we have

__Example__**:** Find the derivative of

We have the given function as

Differentiation with respect to variable , we get

Using the rule, $\frac{d}{{dx}}\left( {\cot x} \right) = - {\csc ^2}x$, we get