Derivative of 3*log(1/x^1-1/x)

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

   1. Let $u = - \frac{1}{x} + \frac{1}{x^{1}}$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- \frac{1}{x} + \frac{1}{x^{1}}\right)$:

      1. Differentiate $- \frac{1}{x} + \frac{1}{x^{1}}$ term by term:

         1. Let $u = x^{1}$.

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

         3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{1}$:

            1. Apply the power rule: $x^{1}$ goes to $1$

            The result of the chain rule is:

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

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

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

            So, the result is: $\frac{1}{x^{2}}$

         The result is: $0$

      The result of the chain rule is:

      $$0$$

   So, the result is: $0$

The answer is:

$$0$$