CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = e^(3x²) + 5^2, then dy/dx at x = 1 is:
By the chain rule, the derivative is 6x·e^(3x²), and the constant term vanishes. At x = 1 the result is 6e³.
- A6e³Correct
- B3e³
- C6e³ + 25
- De³
Explanation
The derivative of e^(3x²) is e^(3x²) × 6x, and the derivative of the constant 25 is 0. At x = 1, dy/dx = 6e³. Option 3e³ forgets the factor 2 from differentiating x², and 6e³ + 25 wrongly keeps the constant.
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