1. The problem is to find the derivative of the function $y = \tan(x)$.\n\n2. The formula for the derivative of the tangent function is $\frac{d}{dx} \tan(x) = \sec^2(x)$.\n\n3. This means the rate of change of $\tan(x)$ with respect to $x$ is $\sec^2(x)$.\n\n4. Therefore, the derivative of $y = \tan(x)$ is $$\frac{dy}{dx} = \sec^2(x).$$\n\n5. This result is important in calculus and trigonometry for understanding how the tangent function behaves and changes.