**The derivative of tan(2x) is equal to two times the secant squared of two times x.** Using mathematical notation, the equation is written as d/dx tan(2x) = 2sec^2(2x).

The derivative of tan(2x) can be found by using the quotient rule and the chain rule. Using the quotient rule, the tangent of 2x can be simplified to read the cosine squared of 2x plus the sine squared of 2x divided by the cosine squared of 2x. Using the Pythagorean identity, this equation further simplifies to one over the cosine squared of 2x. The inverse of cosine squared 2x is the secant squared of 2x. With the chain rule, the derivative of 2x is two.