Derivative of -1/2e^(2x)+c

1. Differentiate $c - \frac{e^{2 x}}{2}$ term by term:

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

      1. Let $u = 2 x$.

      2. The derivative of $e^{u}$ is itself.

      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:

         $$2 e^{2 x}$$

      So, the result is: $- e^{2 x}$

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

   The result is: $- e^{2 x}$

The answer is:

$$- e^{2 x}$$