The derivative of tan(x) can be computed using the quotient rule.
Using the quotient rule, the derivative of tan(x) = d/dx(sin(x)/cos(x)):
= (cos(x) * d/dx(sin(x)) – sin(x) * d/dx(cos(x))) / (cos(x))^2
= (cos(x) * cos(x) – sin(x) * (-sin(x))) / (cos(x))^2
= (cos^2(x) + sin^2(x)) / (cos(x))^2
= 1 / (cos(x))^2
= sec^2(x)
Therefore, the derivative of tan(x) is sec^2(x).
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