CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = x³ ln x... for x > 0, the third derivative d³y/dx³ is:
The third derivative is 6 ln x + 11. The first derivative is 3x² ln x + x², the second is 6x ln x + 5x, and differentiating the second using the product rule gives 6 ln x + 6 + 5, which equals 6 ln x + 11.
- A6 ln x + 11Correct
- B6 ln x + 5
- C6 ln x + 6
- D6 ln x + 11x
Explanation
y' = 3x² ln x + x². y'' = 6x ln x + 3x + 2x = 6x ln x + 5x. y''' = 6 ln x + 6 + 5 = 6 ln x + 11. Option 2 forgets the 6 from differentiating x ln x's product term.
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