Question

знайдіть похідну функції y=x2+3/x+1 ​

Answer 1

Ответ:

$y = \frac{ {x}^{2} + 3 }{x + 1}$

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

Answer 2

Ответ:

(х-1)(х+3)\(х+1)^2