$\frac{dy}{dx}(2y)$

Step 1 ：The question is asking for the derivative of the function $2y$ with respect to $x$. Since $y$ is a function of $x$, we need to use the chain rule to find the derivative. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is $2y$ and the inner function is $y$.

Step 2 ：The derivative of the function $2y$ with respect to $x$ is $2\frac{dy}{dx}$. This is because the derivative of $2y$ with respect to $y$ is $2$, and then we multiply by the derivative of $y$ with respect to $x$, which is $\frac{dy}{dx}$, according to the chain rule.

Step 3 ：Final Answer: $\boxed{{\displaystyle 2\frac{dy}{dx}}}$