Derivative of sqrt(2*x)-3

1. Differentiate $\sqrt{2 x} - 3$ term by term:

   1. Let $u = 2 x$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$:

      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: $2$

      The result of the chain rule is:

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

   4. The derivative of the constant $-3$ is zero.

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

The answer is:

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