Derivative of y=2*e^x+cos(3*x)

1. Differentiate $2 e^{x} + \cos{\left(3 x \right)}$ 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 $e^{x}$ is itself.

      So, the result is: $2 e^{x}$

   2. Let $u = 3 x$.

   3. The derivative of cosine is negative sine:

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

   4. 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:

      $$- 3 \sin{\left(3 x \right)}$$

   The result is: $2 e^{x} - 3 \sin{\left(3 x \right)}$

The answer is:

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