Derivative of 3x-cosx-1

1. Differentiate $3 x - \cos{\left(x \right)} - 1$ 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 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: $\sin{\left(x \right)}$

   3. The derivative of the constant $\left(-1\right) 1$ is zero.

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

The answer is:

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