Derivative of ln(ax)

1. Let $u = a x$.

2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$.

3. Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} a x$:

   1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x$ goes to $1$

      So, the result is: $a$

   The result of the chain rule is:

   $$\frac{1}{x}$$

The answer is: