Derivative of the secant of a fractional 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 secant, we get

Finally, we substitute for u:

 Note that the argument of the secant and tangent in the result is the same as the argument of the secant in the original problem.