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8.. Ifx = exe", then 1+X + 1 (C) 1+...
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8.. Ifx = exe", then 1+X + 1 (C) 1+x x х 1 o cino
JEE/Engineering Exams
Maths
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x=
${e}^{y+{e}^{y+...\infty}}$
$x={e}^{y+(x)}\phantom{\rule{0ex}{0ex}}x={e}^{y+x}\phantom{\rule{0ex}{0ex}}Taking{\mathrm{log}}_{e}bothsides\phantom{\rule{0ex}{0ex}}{\mathrm{log}}_{e}x={\mathrm{log}}_{e}{e}^{y+x}\phantom{\rule{0ex}{0ex}}{\mathrm{log}}_{e}x=y+x\phantom{\rule{0ex}{0ex}}y={\mathrm{log}}_{e}x-x\phantom{\rule{0ex}{0ex}}DifferentiatingBothsidesw.r.tx\phantom{\rule{0ex}{0ex}}\frac{dy}{dx}=\frac{1}{x}-1\phantom{\rule{0ex}{0ex}}\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{x}}\mathbf{=}\mathbf{}\frac{\mathbf{1}\mathbf{-}\mathbf{x}}{\mathbf{x}}$
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