Derivative of 4sqrt(x)-8x

1. Differentiate $4 \sqrt{x} - 8 x$ 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: $\frac{2}{\sqrt{x}}$

   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: $-8$

   The result is: $-8 + \frac{2}{\sqrt{x}}$

The answer is:

$$-8 + \frac{2}{\sqrt{x}}$$