If x=e^{(x/y)},then frac{dy}{dx}= | vedclass

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Question

(C) Given $x = e^{(x/y)}$.Taking natural logarithm on both sides,we get $\log x = \frac{x}{y}$.This implies $y \log x = x$.Differentiating both sides

Vedclass · Accepted Answer

$\frac{x-y}{x \log x}$

Vedclass · Answer

(C) Given $x = e^{(x/y)}$.Taking natural logarithm on both sides,we get $\log x = \frac{x}{y}$.This implies $y \log x = x$.Differentiating both sides with respect to $x$ using the product rule:$\frac{dy}{dx} \cdot \log x + y \cdot \frac{1}{x} = 1$.Multiplying the entire equation by $x$:$x \log x \cdot \frac{dy}{dx} + y = x$.Rearranging the terms to solve for $\frac{dy}{dx}$:$x \log x \cdot \frac{dy}{dx} = x - y$.Therefore,$\frac{dy}{dx} = \frac{x-y}{x \log x}$.

If $x=e^{(x/y)}$,then $\frac{dy}{dx}=$

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