Derivative of -sqrt(x)+3*x-7

1. Differentiate $\left(- \sqrt{x} + 3 x\right) - 7$ term by term:

   1. Differentiate $- \sqrt{x} + 3 x$ term by term:

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

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

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

      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: $3$

      The result is: $3 - \frac{1}{2 \sqrt{x}}$

   2. The derivative of the constant $-7$ is zero.

   The result is: $3 - \frac{1}{2 \sqrt{x}}$

The answer is:

$$3 - \frac{1}{2 \sqrt{x}}$$