Derivative of exp(3*x)+3*exp(x)

1. Differentiate $e^{3 x} + 3 e^{x}$ term by term:

   1. Let $u = 3 x$.

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

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

      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: $3$

      The result of the chain rule is:

      $$3 e^{3 x}$$

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

      1. The derivative of $e^{x}$ is itself.

      So, the result is: $3 e^{x}$

   The result is: $3 e^{3 x} + 3 e^{x}$

2. Now simplify:

   $$3 \left(e^{2 x} + 1\right) e^{x}$$

The answer is:

$$3 \left(e^{2 x} + 1\right) e^{x}$$