1. The problem asks us to differentiate the function $y=\tan x$. 2. Recall that the derivative of $\tan x$ with respect to $x$ is a standard derivative result from calculus. 3. Using the identity $\tan x = \frac{\sin x}{\cos x}$, we apply the quotient rule or remember the derivative formula directly. 4. The derivative of $\tan x$ is known to be $\sec^2 x$. 5. Thus, $$\frac{d}{dx} \tan x = \sec^2 x.$$