What is the derivative of f(x) = 4/x? (2022)

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Question: What is the derivative of f(x) = 4/x? (2022)

Options:

Correct Answer: -4/x^2

Exam Year: 2022

Solution:

Using the power rule, f\'(x) = -4/x^2.

What is the derivative of f(x) = 4/x? (2022)

What is the derivative of f(x) = 4/x? (2022)

Step 1: Rewrite the function f(x) = 4/x in a different form. This can be done by expressing it as f(x) = 4 * x^(-1).
Step 2: Identify the power of x in the rewritten function. Here, the power is -1.
Step 3: Apply the power rule for derivatives. The power rule states that if f(x) = x^n, then f'(x) = n * x^(n-1).
Step 4: For our function, apply the power rule: f'(x) = -1 * 4 * x^(-1-1).
Step 5: Simplify the expression. This gives us f'(x) = -4 * x^(-2).
Step 6: Rewrite the result in a more standard form. This results in f'(x) = -4/x^2.

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