Derivative of y=3x-1/2x+5

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

   1. Differentiate $- \frac{x}{2} + 3 x$ 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: $x$ goes to $1$

         So, the result is: $3$

      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: $- \frac{1}{2}$

      The result is: $\frac{5}{2}$

   2. The derivative of the constant $5$ is zero.

   The result is: $\frac{5}{2}$

The answer is:

$$\frac{5}{2}$$