If x = e y + e y + e y + e y + ⋯ ∞ Options: A . &nbsp1x B . &nbsp1−xx C . &nbspx1+x D . &nbspNone of these

Answer: Option B : B x = e y + x ⇒ l o g e x = y + x ∴ 1 x = d y d x + 1 ⇒ d y d x = 1 − x x

If x=ey+ey+ey+ey+⋯∞

Question

x = e^{y + e^{y + e^{y + e^{y + \dots \infty}}}}

Options:

A . 1x

B . 1−xx

C . x1+x

D . None of these

Answer: Option B
:
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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