Derivative of log(3)/((5*x))

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

   1. Let $u = 5 x$.

   2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$:

      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: $5$

      The result of the chain rule is:

      $$- \frac{1}{5 x^{2}}$$

   So, the result is: $- \frac{\log{\left(3 \right)}}{5 x^{2}}$

The answer is:

$$- \frac{\log{\left(3 \right)}}{5 x^{2}}$$