The derivative of sec(x) can be found using the quotient rule and trigonometric identities.
Recall that:
sec(x) = 1/cos(x)
Using the quotient rule, we get:
d/dx(sec(x)) = [cos(x)(-1/cos^2(x))] / [cos(x)^2]
Simplifying, we get:
d/dx(sec(x)) = -sin(x)/cos^2(x)
Using the identity 1 + tan^2(x) = sec^2(x), we can rewrite cos^2(x) as 1 + tan^2(x).
So the final result is:
d/dx(sec(x)) = -sec(x)tan(x)
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