Derivative of 5e^(3*x+7)

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

   1. Let $u = 3 x + 7$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 7\right)$:

      1. Differentiate $3 x + 7$ term by term:

         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: $3$

         2. The derivative of the constant $7$ is zero.

         The result is: $3$

      The result of the chain rule is:

      $$3 e^{3 x + 7}$$

   So, the result is: $15 e^{3 x + 7}$

2. Now simplify:

   $$15 e^{3 x + 7}$$

The answer is:

$$15 e^{3 x + 7}$$