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Derivative

If x=ey+ey+ey...

Question

If x = $e^{y + e^{y + e^{y + e^{y + . . . \infty}}}}$ , then $\frac{d y}{d x}$ is

A

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B

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C

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D

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

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Solution

The correct option is B

x = $e^{y + x}$ $\Rightarrow l o g_{e} x$ = y + x

$∴ \frac{1}{x}$ = $\frac{d y}{d x} + 1$

$\Rightarrow \frac{d y}{d x}$ = $\frac{1 - x}{x}$

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