**The derivative of ln(3x) is one over x.** The symbol ln is used for a natural log function. The derivative of ln(3x) is expressed as f'(x) equals ln(3x)

The expression ln(3x) can be separated as ln(x) plus ln(3). The derivative of ln(3) is zero, because ln(3) is a constant, and the derivative of a constant is always zero. The derivative of x is always one over x, based on the rule that for f(x) = ln(x), the derivative is f(x) = 1/x.

Another way to solve for the derivative of ln(3x) is to substitute a variable for 3x, and multiply the derivative of the variable by the derivative of the natural log of the variable.