Q:

10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE

Accepted Solution

A:
f'(x) = (d/dx)(arcsec(x) -arccsc(x)) = 1/(x^2*√(1 -1/x^2)) -(-1)/(x^2*√(1 -1/x^2))

a) f'(x) = (d/dx)(arcsec(x) -arccsc(x)) = 2/√(x^4 -x^2)

b) f'(4) = 2/√(4^4 -4^2) = 2/√240 = (√15)/30

c) f'(-1) = 2/√((-1)^4 -(-1)^2) = 2/0 = undefined

d) f'(1/2) = 2/√((1/2)^4 -(1/2)^2) = 2/√(-3/16) = 8/√-3 = -i(8/3)√3