Question

Y= e^x-1/ e^x+1 resolver

Answer 1

$y \: = \: \frac{ {e}^{x} \: - \: 1 }{ {e}^{x} \: + \: 1}$

$y' \: = \: \frac{d}{dx} ( \frac{ {e}^{x} \: - \: 1}{ {e}^{x} \: + \: 1 })$

$y' \: = \: \frac{ \frac{d}{dx} ( {e}^{x} \: - \: 1) \: \times \:( {e}^{x} \: + \: 1) \: - \: ( {e}^{x} \: - \: 1) \: \times \: \frac{d}{dx} ( {e}^{x} \: + \: 1)}{( {e}^{x} \: + \: 1) ^{2} }$

$y' \: = \: \frac{ {e}^{x} \: \times \:( {e}^{x} \: + \: 1) \: - \:( {e}^{x} \: - \: 1) {e}^{x} }{( {e}^{x} \: - \: 1) ^{2} }$

$\boxed{ \bold{y' \: = \: \frac{2 {e}^{x} }{( {e}^{x} \: + \: 1) ^{2} } }}$

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