Derivative of y=12x+√x

1. Differentiate $\sqrt{x} + 12 x$ 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: $12$

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

   The result is: $12 + \frac{1}{2 \sqrt{x}}$

The answer is:

$$12 + \frac{1}{2 \sqrt{x}}$$