Differentiate the function y = ln(3x).

The derivative of y = ln(3x) is 1/x.

To differentiate y = ln(3x), we use the chain rule. Let u = 3x, then y = ln(u). Using the chain rule, we have:

dy/dx = dy/du * du/dx

To find dy/du, we use the derivative of ln(u), which is 1/u. Therefore:

dy/du = 1/u

To find du/dx, we differentiate u = 3x with respect to x, giving:

du/dx = 3

Substituting these values back into the chain rule equation, we have:

dy/dx = dy/du * du/dx
= 1/u * 3
= 3/3x
= 1/x

Therefore, the derivative of y = ln(3x) is 1/x. For a more foundational understanding, you can review the Introduction to Derivatives. Additionally, it's helpful to familiarise yourself with the Basic Differentiation Rules. For further exploration of logarithmic functions in calculus, refer to Differentiation of Exponential and Logarithmic Functions.