CUET · MATHS · PYQ PAPER 2025
If \(y=5 e^{2 x}+4 e^{3 x}\), then \(\frac{d^2 y}{d x^2}\) equals:
- A \(3\left(2 e^{2 x}+6 e^{3 x}\right)\)
- B \(4\left(5 e^{2 x}+9 e^{3 x}\right)\)
- C \(5\left(4 e^{2 x}+9 e^{3 x}\right)\)
- D \(2\left(5 e^{2 x}+8 e^{3 x}\right)\)
Answer & Solution
Correct Answer
(B) \(4\left(5 e^{2 x}+9 e^{3 x}\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = 5(2e^{2x}) + 4(3e^{3x}) = 10e^{2x} + 12e^{3x}\) \(\frac{d^2y}{dx^2} = 10(2e^{2x}) + 12(3e^{3x}) = 20e^{2x} + 36e^{3x}\) \(= 4(5e^{2x} + 9e^{3x})\)
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