Derivative of sin(x)+3x+1

1. Differentiate $\left(3 x + \sin{\left(x \right)}\right) + 1$ term by term:

   1. Differentiate $3 x + \sin{\left(x \right)}$ term by term:

      1. The derivative of sine is cosine:

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

      2. 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 is: $\cos{\left(x \right)} + 3$

   2. The derivative of the constant $1$ is zero.

   The result is: $\cos{\left(x \right)} + 3$

The answer is:

$$\cos{\left(x \right)} + 3$$