d/dx (log_a x)

Given: The derivative is given as: d/dx (log_ax).

Concept Used:

The logarithmic differentiation rule:

For a logarithm with a base a, the derivative of log_ax is:

d/dx (log_ax) = 1 / (x ln a)

Here, ln a refers to the natural logarithm of a.

Calculation:

1. Using the formula for logarithmic differentiation:

d/dx (log_ax) = 1 / (x ln a)

2. Comparing this with the provided options:

Option 2 matches the result: 1 / (x ln a)

Conclusion:

∴ The correct answer is Option 2.