Final answer:
The derivative of the function f(x) = x - √{x} is f'(x) = 1 - (1/2)x^(-1/2), which simplifies to f'(x) = 1 - (1/2√{x}). The correct answer is B) f'(x) = -1/2√{x}.
Step-by-step explanation:
The student is asking about finding the derivative of the function f(x) = x - √{x}. To find this derivative, we'll apply the rules of differentiation to each term separately. The derivative of x with respect to x is 1, and the derivative of √{x} (which is x^(1/2)) with respect to x is 1/2x^(-1/2), which we can write as (-1/2)√{x} after applying the chain rule. Combining these gives us:
f'(x) = 1 - ½(√{x})' = 1 - (½√{x}) = 1 - ½/x^(1/2)
Therefore, the correct answer is B) f'(x) = -1/2√{x}.