Q:

What is the derivative of ln(3x)?

A:

Quick Answer

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)

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Full Answer

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.

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