Final answer:
The derivative of the function 2cos(x) - 1 is -2sin(x), using basic differentiation rules for trigonometric functions.
Step-by-step explanation:
To find the derivative of the function 2cos(x) - 1, we can use the basic differentiation rules for trigonometric functions. The derivative of cos(x) with respect to x is -sin(x). So, when we take the derivative of 2cos(x), we need to apply the constant multiplier rule, which tells us to multiply the derivative of cos(x) by the constant 2.
Thus, the derivative of 2cos(x) is -2sin(x). Since the derivative of a constant is zero, the derivative of -1 is 0. Combining these, the derivative of 2cos(x) - 1 is -2sin(x).
Looking at the provided options, the correct answer is option B: -2sin(x).