If $x=e^{\left(\frac{x}{y}\right)}$, then $\frac{d y}{d x}=$

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Aicharya · Accepted Answer

$x=e^{\left(\frac{x}{y}\right)} \Rightarrow \log _e x=\frac{x}{y} \Rightarrow y \log _e x=x$ Differentiating both sides w.r.t $x$ we get $\frac{d y}{d x} \cdot \log _e x+y \cdot \frac{1}{x}=1$ $\Rightarrow \frac{d y}{d x} \cdot x \log _e x+y=x$ $\Rightarrow \frac{d y}{d x}=\frac{x-y}{x \log _e x}$ Change the option (C) as $\frac{x-y}{x \log x}$

If $x=e^{\left(\frac{x}{y}\right)}$, then $\frac{d y}{d x}=$

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