If $y = 5e^{2x}+4e^{3x}$, then $\frac{d^2y}{dx^2}$ equals:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $4(5e^{2x}+9e^{3x})$
Given: $y = 5e^{2x} + 4e^{3x}$
First derivative:
$\frac{dy}{dx} = 5 \cdot 2e^{2x} + 4 \cdot 3e^{3x} = 10e^{2x} + 12e^{3x}$
Second derivative:
$\frac{d^2y}{dx^2} = 10 \cdot 2e^{2x} + 12 \cdot 3e^{3x} = 20e^{2x} + 36e^{3x}$