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The derivative of y = tan(x) is sec^2(x).

To differentiate y = tan(x), we can use the quotient rule. Let u = sin(x) and v = cos(x). Then, y = u/v. Using the quotient rule, we have:

y' = (v*u' - u*v')/v^2

Since u = sin(x) and v = cos(x), we have u' = cos(x) and v' = -sin(x). Substituting these values, we get:

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

Simplifying, we get:

y' = (cos^2(x) + sin^2(x))/cos^2(x)

Using the identity cos^2(x) + sin^2(x) = 1, we get:

y' = 1/cos^2(x)

Since sec(x) = 1/cos(x), we can write:

y' = sec^2(x)

Therefore, the derivative of y = tan(x) is sec^2(x).

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