Derivative of the cotangent of a quotient:

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 cotangent, we get

Finally, we substitute for u:

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