If x = e^{y + e^{y + dots infty}},x 0,then | vedclass

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(C) Given the equation $x = e^{y + e^{y + \dots \infty}}$.Since the exponent is an infinite series,we can write it as $x = e^{y + x}$.Taking the natur

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$\frac{1 - x}{x}$

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(C) Given the equation $x = e^{y + e^{y + \dots \infty}}$.Since the exponent is an infinite series,we can write it as $x = e^{y + x}$.Taking the natural logarithm on both sides,we get $\ln(x) = y + x$.Now,differentiate both sides with respect to $x$:$\frac{d}{dx}(\ln(x)) = \frac{d}{dx}(y + x)$$\frac{1}{x} = \frac{dy}{dx} + 1$.Rearranging the terms to solve for $\frac{dy}{dx}$:$\frac{dy}{dx} = \frac{1}{x} - 1 = \frac{1 - x}{x}$.

If $x = e^{y + e^{y + \dots \infty}}$,$x > 0$,then $\frac{dy}{dx}$ is

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