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If $y = 5e^{2x}+4e^{3x}$, then $\frac{d^2y}{dx^2}$ equals: |
$3(2e^{2x}+6e^{3x})$ $4(5e^{2x}+9e^{3x})$ $5(4e^{2x}+9e^{3x})$ $2(5e^{2x}+8e^{3x})$ |
$4(5e^{2x}+9e^{3x})$ |
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: $\frac{d^2y}{dx^2} = 10 \cdot 2e^{2x} + 12 \cdot 3e^{3x} = 20e^{2x} + 36e^{3x}$ |
