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Question: If \(x = e^{y + e^{y + e^{y + e^{y + ....\infty}}}}\), then \(\frac{dy}{dx}\) is...

If x=ey+ey+ey+ey+....∞x = e^{y + e^{y + e^{y + e^{y + ....\infty}}}}, then dydx\frac{dy}{dx} is

A

x1+x\frac{x}{1 + x}

B

1x\frac{1}{x}

C

1−xx\frac{1 - x}{x}

D

None of these

Answer

1−xx\frac{1 - x}{x}

Explanation

Solution

x = ey+x

Ž log x = (y + x) . 1

Ž dydx=1x\frac{dy}{dx} = \frac{1}{x} – 1