Derivative of y=logx+ax

1. Differentiate $a x + \log{\left(x \right)}$ term by term:

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

   2. 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 is: $a + \frac{1}{x}$

The answer is:

$$a + \frac{1}{x}$$