Derivative of e^(2x)+e^(3x)

1. Differentiate $e^{3 x} + e^{2 x}$ term by term:

   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:

      $$2 e^{2 x}$$

   4. Let $u = 3 x$.

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

   6. 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:

      $$3 e^{3 x}$$

   The result is: $3 e^{3 x} + 2 e^{2 x}$

2. Now simplify:

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

The answer is:

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