The derivative of sec(x) can be found using the quotient rule method. Recall that sec(x) is the reciprocal of cos(x), i.e., sec(x) = 1/cos(x). Hence,
(d/dx) sec(x) = (d/dx) [1/cos(x)]
Applying the quotient rule, we get:
= [(-1/cos^2(x)) * (-sin(x))] / [cos^2(x)]
= sin(x) / cos^2(x)
= sin(x) * sec^2(x)
Thus, the derivative of sec(x) is sin(x) times the square of sec(x), i.e., sec(x)^2.
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