Let’s enhance the clarity and readability of the content, ensuring proper formatting for mathematical expressions.

To find the derivative of the function $y = \cot(4x)$, we will use the chain rule.

First, we can introduce a substitution to simplify our calculations. Let $u = 4x$. Consequently, we can rewrite our function as $y = \cot(u)$.

According to the chain rule, the derivative of $y$ with respect to $x$ can be expressed as:

Next, we need to compute $\frac{dy}{du}$. The derivative of $\cot(u)$ is given by:

Substituting back for $u$, we have:

Now, we determine $\frac{du}{dx}$. The derivative of $u$ with respect to $x$ is:

We can now substitute both derivatives back into our chain rule expression:

Simplifying this expression, we obtain:

Thus, we conclude that the derivative of $y = \cot(4x)$ is:

This presentation enhances clarity and maintains proper formatting for mathematical expressions while slightly rephrasing the content for improved readability.