Differentiate the function y = ln(2x).

The derivative of y = ln(2x) is 1/x.

To differentiate y = ln(2x), we use the chain rule. Let u = 2x, then y = ln(u). Using the chain rule, we have:

dy/dx = dy/du * du/dx

Since dy/du = 1/u and du/dx = 2, we have:

dy/dx = 1/u * 2

Substituting back in for u, we get:

dy/dx = 1/(2x) * 2

Simplifying, we get:

dy/dx = 1/x

Therefore, the derivative of y = ln(2x) is 1/x.