Derivative of Arc Secant

1. Oct 17, 2006

wazzup

Hello there

In the derivative of the arc secant, why is the absolute value of x ( which is present in the denominator) taken? Is this to prevent the possible of having a zero ( and making the whole expression undefined ? )

Thanks

2. Oct 18, 2006

HallsofIvy

Staff Emeritus
No, absolute value won't do that: |0|= 0 so you still can have in the denominator. (And the derivative is undefined for x= 0.) Strictly speaking the inverse secant is only defined for x less than -1 or greater than 1. It is because of the square root in the derivative that we have a "plus or minus" which, combined with x itself, makes the derivative always positive.