Derivative of x^2-5x+lnx-3

1. Differentiate $\left(\left(x^{2} - 5 x\right) + \log{\left(x \right)}\right) - 3$ term by term:

   1. Differentiate $\left(x^{2} - 5 x\right) + \log{\left(x \right)}$ term by term:

      1. Differentiate $x^{2} - 5 x$ term by term:

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

         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: $-5$

         The result is: $2 x - 5$

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

      The result is: $2 x - 5 + \frac{1}{x}$

   2. The derivative of the constant $-3$ is zero.

   The result is: $2 x - 5 + \frac{1}{x}$

The answer is:

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