If y = sin(log_e x), then x^2 frac{d^2 y}{dx^ | vedclass

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(D) Given that, $y = \sin(\log_e x)$ $(i)$ On differentiating with respect to $x$, we get $\frac{dy}{dx} = \cos(\log_e x) \cdot \frac{1}{x}$ $x \frac{

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$-y$

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(D) Given that, $y = \sin(\log_e x)$ $(i)$ On differentiating with respect to $x$, we get $\frac{dy}{dx} = \cos(\log_e x) \cdot \frac{1}{x}$ $x \frac{dy}{dx} = \cos(\log_e x)$ Again differentiating with respect to $x$, we get $x \frac{d^2 y}{dx^2} + \frac{dy}{dx} = -\sin(\log_e x) \cdot \frac{1}{x}$ Multiplying both sides by $x$, we get $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} = -\sin(\log_e x)$ Since $y = \sin(\log_e x)$, we have $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} = -y$

If $y = \sin(\log_e x)$, then $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx}$ is equal to

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