The derivative of sec(x) can be found using the quotient rule and the chain rule.
sec(x) = 1/cos(x)
Thus, we have:
d/dx [sec(x)] = d/dx [1/cos(x)]
Using the quotient rule, we get:
= [(-1/cos^2(x)) * (-sin(x))] / cos(x)^2
= sin(x) / cos^2(x)
Using the identity, tan(x) = sin(x) / cos(x), we can rewrite this as:
d/dx [sec(x)] = tan(x) * sec(x)
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