Question

Найдите производную функции ​

Answer 1

Ответ:

б)

$f'(x) = \sqrt{2} \times 2x - (3x - 2)'(5x + 1) - (5x + 1)'(3x - 2) = \\ = 2 \sqrt{2} x - 3(5x + 1) - 5(3x - 2) = \\ = 2 \sqrt{2} x - 15x - 3 - 15x + 10 = \\ = - 30x + 2 \sqrt{2} x + 7 = \\ = (2 \sqrt{2} - 30)x + 7$

г)

$f'(x) = \frac{(3x - {x}^{2} )'(x + 2) - (x + 2)'(3x - {x}^{2}) }{ {(x + 2)}^{2} } = \\ = \frac{(3 - 2x)(x + 2) - 1 \times (3x - {x}^{2}) }{ {(x + 2)}^{2} } = \\ = \frac{3x + 6 - 2 {x}^{2} - 4x - 3x + {x}^{2} }{ {(x + 2)}^{2} } = \\ = \frac{ - {x}^{2} - 4x + 6}{ {(x + 2)}^{2} } = - \frac{ {x}^{2} + 4x - 6 }{ {(x + 2)}^{2} }$