If $y = 8e^{9x}+6e^{-9x},$ then which of the following is the value of $\frac{d^2y}{dx^2}$ ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $81 y$
$\frac{dy}{dx}=\frac{d(8e^{9x}+6e^{-9x})}{dx}=72e^{9x}-54e^{-9x}$
$\frac{d^2y}{dx^2}=9×72e^{9x}+45×9e^{-9x}$
$=81(8e^{9x}+6e^{-9x})=81y$