We shall prove formula for derivative of cosecant 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 in the above equation, we get
Taking LCM (Least Common Factor), 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, , we get