If f(x) = x² ln x for x > 0, what is f'(x)?
Correct answer: D. 2x ln x + x
- A. x ln x + 2x
- B. x²/x
- C. 2x + ln x
- D. 2x ln x + x
Explanation
The product rule gives f'(x) = 2x ln x + x²(1/x), which simplifies to 2x ln x + x. The option x²/x is only the derivative of ln x multiplied by x² and omits the other product-rule term.
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Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
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