Derivative of x-3sqrt(x)

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

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

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

      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: $\frac{3}{2 \sqrt{x}}$

      So, the result is: $- \frac{3}{2 \sqrt{x}}$

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

The answer is:

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