CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = x² eˣ, then the value of dy/dx at x = 1 is:
The derivative at x = 1 is 3e. Using the product rule, d/dx of x²eˣ is eˣ(x² + 2x). At x = 1 this becomes e(1 + 2) = 3e, because both the term from differentiating x² and the term from differentiating eˣ must be included.
- Ae
- B2e
- C3eCorrect
- D4e
Explanation
By the product rule, dy/dx = 2x·eˣ + x²·eˣ = eˣ(x² + 2x). At x = 1 this is e(1 + 2) = 3e. The value 2e comes from using only 2x·eˣ, and e comes from using only x²·eˣ.
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