CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = x³ log x (natural logarithm), then dy/dx at x = e is:
By the product rule, dy/dx = x² + 3x² log x. Substituting x = e where log e = 1 gives e² + 3e² = 4e². The answer is 4e².
- A4e²Correct
- Be²
- C3e²
- D4e³
Explanation
Product rule: dy/dx = x³·(1/x) + 3x²·log x = x² + 3x² log x. At x = e, log e = 1, so dy/dx = e² + 3e² = 4e². Option e² comes from forgetting the second product term.
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