If y = e^ x + e^ x + e^ x + .... , then dy dx = - Vidyadip

MCQ

If $y = {e^{x + {e^{x + {e^{x + ....\infty }}}}}}$, then ${{dy} \over {dx}} = $

✓
${y \over {1 - y}}$
B
${1 \over {1 - y}}$
C
${y \over {1 + y}}$
D
${y \over {y - 1}}$

✓

Answer

Correct option: A.

${y \over {1 - y}}$

a
(a) $y = {e^{x + y}}$ ==> $\log y = (x + y)\log e$

==> $\frac{1}{y}\frac{{dy}}{{dx}} = 1 + \frac{{dy}}{{dx}}$

==> $ \frac{{dy}}{{dx}} = \frac{y}{1-y} $.

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