Question

Помогите, пожалуйста
Найти значение производной

Answer 1

Пошаговое объяснение:

$\: \: ( \frac{u}{v} )' = \frac{u'v - uv'}{v {}^{2} } \\y = \frac{7x - {x}^{2} }{x - 3} \\ y' = \frac{(7x - {x}^{2}) '(x - 3) - (7x - {x}^{2})(x - 3)'}{ {(x - 3)}^{2} } \\ y' = \frac{(7- 2{x}) (x - 3) - (7x - {x}^{2})(1 - 0)}{ {(x - 3)}^{2} } \\ y' = \frac{(7x- 2{x} ^{2} - 21 + 6x) - (7x - {x}^{2})}{ {(x - 3)}^{2} }\\ y' = \frac{ - {x} ^{2} + 6x - 21}{ {(x - 3)}^{2} }$

Можно записать след.образом

$y' = \frac{ -( {x} ^{2} - 6x + 21)}{ {(x - 3)}^{2} } \\ y' = \frac{ -( {x} ^{2} - 6x + 9 + 12)}{ {(x - 3)}^{2} } \\ y' = \frac{ - {(x - 3)} ^{2} - 12}{ {(x - 3)}^{2} } \\ y' = - 1 - \frac{ 12}{ {(x - 3)}^{2} }$