Derivative of the sine 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 sine, we get

Finally, we substitute for u:

Note that the argument of the cosine in the result is the same as the argument of the sine in the original problem.