Question

НАЙДИТЕ ПРОИЗВОДНУЮ​

Answer 1

а)

$y' = 20 {x}^{3 } - 20$

б)

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

в)

$y' =2 \times \frac{1}{2 \sqrt{x} } + 18 {x}^{2} = \\ = \frac{1}{ \sqrt{x} } + 18 {x}^{2}$

г)

$y' = \frac{1}{4} \times \frac{1}{2 \sqrt{x} } + 25 {x}^{4} + 2 \times \frac{1}{ {x}^{2} } = \\ = \frac{1}{8 \sqrt{x} } + 25 {x}^{4} + \frac{2}{ {x}^{2} }$

д)

$y' =(2 {x}^{3} + 5x)' (6x - 5) + (2 {x}^{3} + 5x)(6x - 5)' = \\ = (6 {x}^{2} + 5)(6x - 5) + 6(2 {x}^{3} + 5x) = \\ = 36 {x}^{3} - 30 {x}^{2} + 30x - 25 + 12 {x}^{3} + 30x = \\ = 48 {x}^{3} - 30 {x}^{2} + 60x - 25$

е)

$y ' = \frac{(2x + 3)'(x - 2) - (2x + 3)(x - 2)'}{ {(x - 2)}^{2} } = \\ = \frac{x(x - 2) - (2x + 3)}{ {(x - 2)}^{2} } = \\ = \frac{ {x}^{2} - 2x- 2x - 3}{ {(x - 2)}^{2} } = \\ = \frac{ {x}^{2} - 4x - 3}{ {(x - 2)}^{2} }$

ж)

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