Derivative of xlnx-0,03

1. Differentiate $x \log{\left(x \right)} - \frac{3}{100}$ term by term:

   1. Apply the product rule:

      $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

      $f{\left(x \right)} = x$; to find $\frac{d}{d x} f{\left(x \right)}$:

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

      $g{\left(x \right)} = \log{\left(x \right)}$; to find $\frac{d}{d x} g{\left(x \right)}$:

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

      The result is: $\log{\left(x \right)} + 1$

   2. The derivative of the constant $- \frac{3}{100}$ is zero.

   The result is: $\log{\left(x \right)} + 1$

The answer is:

$$\log{\left(x \right)} + 1$$