Question

: REGLAS DE DERIVACION

Answer 1

Tema: Derivación

$y \: = \: 3 \: - \: \frac{ \frac{1}{x} }{x \: + \: 5}$

$y' \: = \: \frac{d}{dx} (3 \: - \: \frac{1}{x \: \times \: (x \: + \: 5)} )$

$y' \: = \: \frac{d}{dx} (3 \: - \: \frac{1}{ {x}^{2} \: + \: 5x } )$

$y' \: = \: \frac{d}{dx} (3) \: - \: \frac{d}{dx} ( \frac{1}{ {x}^{2} } \: + \: 5)$

$y' \: = \: 0 \: - \: ( - \frac{2x \: + \: 5}{( {x}^{2} \: + \: 5) ^{2} } )$

$\boxed{ \bold{y' \: = \: \frac{2x \: + \: 5}{( {x}^{2} \: + \: 5x) ^{2} } }}$

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