Derivative of 8cosx+e^x

1. Differentiate $e^{x} + 8 \cos{\left(x \right)}$ term by term:

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

      1. The derivative of cosine is negative sine:

         $$\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$$

      So, the result is: $- 8 \sin{\left(x \right)}$

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

   The result is: $e^{x} - 8 \sin{\left(x \right)}$

The answer is:

$$e^{x} - 8 \sin{\left(x \right)}$$