The function is:

\[
f(x) = 2x - \cos(x)
\]

To find the derivative, we differentiate each term:

1. The derivative of \( 2x \) with respect to \( x \) is \( 2 \).
2. The derivative of \( -\cos(x) \) is \( \sin(x) \) because the derivative of \( \cos(x) \) is \( -\sin(x) \).

Thus, the derivative of \( f(x) = 2x - \cos(x) \) is:

\[
f'(x) = 2 + \sin(x)
\]

Let me know if you need further explanation or have questions.

### Related questions:
1. What is the second derivative of \( f(x) = 2x - \cos(x) \)?
2. How would the derivative change if the function was \( 2x + \cos(x) \)?
3. How do you find the derivative of more complex trigonometric functions like \( \sin(2x) \)?
4. What is the geometric interpretation of the derivative \( 2 + \sin(x) \)?
5. How do derivatives apply to real-world problems?

### Tip:
Always remember, the derivative of a sum or difference of functions is the sum or difference of their derivatives.

Find the derivative of the function f(x) = 2x - cos(x) with detailed steps. This solution covers the sum rule of differentiation and the derivatives of basic trigonometric functions. Suitable for high school and college calculus students.

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