Using the chain rule and the derivative of the secant function, we can find the derivative of sec(x) with respect to x:
Let y = sec(x)
Then,
dy/dx = d/dx(sec(x)) = d/dx(1/cos(x))
= (-1/cos^2(x)) * d/dx(cos(x))
= (-1/cos^2(x)) * (-sin(x))
= sin(x)/cos^2(x)
= sin(x) * sec^2(x)
Therefore, the derivative of sec(x) with respect to x is sin(x) * sec^2(x).
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