Final answer:
The derivative of f(x) = -x + 1 is f'(x) = -1.
Step-by-step explanation:
The derivative of a function represents the rate at which the function is changing at any given point. To find the derivative of a function, we can use the power rule, which states that if a function is of the form f(x) = ax^n, then its derivative is f'(x) = nax^(n-1).
In this case, the function f(x) = -x + 1 is a linear function, so its derivative will be a constant. The derivative of -x is -1, and the derivative of a constant is 0. Therefore, the derivative of f(x) = -x + 1 is f'(x) = -1.
The derivative, f'(x), of the function f(x) = -x + 1 is found by differentiating each term of the function with respect to x. The derivative of a constant term (like 1) is 0 and the derivative of -x with respect to x is -1. Hence, the derivative of the function is just f'(x) = -1.