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Differentiate the function y = sec(x).

The derivative of y = sec(x) is y' = sec(x)tan(x).

To differentiate y = sec(x), we use the quotient rule. Let u = 1 and v = cos(x). Then, using the formula for the quotient rule, we have:

y' = (u'v - v'u) / v^2
= (0*cos(x) - (-sin(x)*1)) / cos^2(x)
= sin(x) / cos^2(x)

Next, we use the identity sec(x) = 1/cos(x) to simplify the expression:

y' = sin(x) / cos^2(x)
= sin(x) * sec^2(x)

Finally, we use the identity tan(x) = sin(x) / cos(x) to write the answer in terms of sec(x) and tan(x):

y' = sin(x) * sec^2(x)
= sec(x) * sin(x) / cos^2(x)
= sec(x) * tan(x)

Therefore, the derivative of y = sec(x) is y' = sec(x)tan(x).

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