Derivative of the cosecant of an integral power:

Via the Scalar Multiple rule, we can treat this as.

We can go a step further and consider it as involving a quantity u:

, where .

When we eventually apply the Chain Rule, we'll need

.

Combining these partial results and using the derivative of the cosecant, we get

Finally, we substitute for u:

Note that the argument of the cosecant and cotangent in the result is the same as the argument of the cosecant in the original problem.