Derivative of 2^(x+3)

1. Let $u = x + 3$.

2. $\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 3\right)$:

   1. Differentiate $x + 3$ term by term:

      1. Apply the power rule: $x$ goes to $1$

      2. The derivative of the constant $3$ is zero.

      The result is: $1$

   The result of the chain rule is:

   $$2^{x + 3} \log{\left(2 \right)}$$

4. Now simplify:

   $$2^{x + 3} \log{\left(2 \right)}$$

The answer is:

$$2^{x + 3} \log{\left(2 \right)}$$