Derivative of e^(5*x)+10*x

1. Differentiate $10 x + e^{5 x}$ term by term:

   1. Let $u = 5 x$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$:

      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: $5$

      The result of the chain rule is:

      $$5 e^{5 x}$$

   4. 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: $10$

   The result is: $5 e^{5 x} + 10$

The answer is:

$$5 e^{5 x} + 10$$