Final answer:
To find f'(5) for the function f(x) = 4/x, we calculated the general derivative and then evaluated it at x=5, yielding a direct answer of -4/25.
Step-by-step explanation:
The student aims to find the derivative of the function f(x) = 4/x at the point x=5. To compute f'(5), we first determine the general form of the derivative of f(x) and then substitute x with 5.
To find the derivative of f(x), we apply the power rule, which states that the derivative of x^n is n*x^(n-1). Since f(x) = 4/x can be rewritten as 4*x^(-1), its derivative f'(x) is -4*x^(-2) or -4/x^2. Therefore, f'(5) equals -4/(5^2), which simplifies to -4/25.
The calculation step is as follows: f'(x) = -4*x^(-2), and f'(5) = -4*5^(-2) = -4/25. This calculation provides us with a direct answer of -4/25 for the original question.