Differentiation of the inverse secant:
exponential argument: Find ![]()
We shall use the Differentiation Rule for the arcsec and the Chain Rule:
Let
,
.
After substituting, we have

Since
is always positive, we can remove the absolute value signs and cancel, getting

Review Note: Squaring the exponential involves the addition of the exponents. The exponent of x remains 2 in the denominator.