If f(x) = ln(x^2 + 1), what is f'(x)?
Answer and explanation
Correct answer: B. 2x / (x^2 + 1)
- Step 1: Apply the chain rule for logarithmic functions: d/dx [ln(u)] = u' / u.
- Step 2: Here u = x^2 + 1, so u' = 2x.
- Step 3: Therefore, f'(x) = 2x / (x^2 + 1).
Answer
2x / (x^2 + 1).
Why not the others: '1 / (x^2 + 1)' forgets to multiply by the derivative of the inner function (2x); '2x * (x^2 + 1)' multiplies instead of dividing by u; '2 / (x^2 + 1)' drops the variable x in the numerator.
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