Question

Производная сложной функции.найти по формуле u'v-v'u/u^2​

Answer 1

5.

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

6.

$y '= \frac{(2 {x}^{2} )'(3 - x) - (3 - x)' \times 2 {x}^{2} }{ {(3 - x)}^{2} } = \\ = \frac{4x( 3 - x) + 1 \times 2 {x}^{2} }{ {(3 - x)}^{2} } = \\ = \frac{12x - 4 {x}^{2} + 2 {x}^{2} }{ {(3 - x)}^{2} } = \frac{ - 2 {x}^{2} + 12x}{ {(3 - x)}^{2} } = \\ = \frac{2x(6 - x)}{ {(3 - x)}^{2} }$

7.

$y' = \frac{(4x)'(2x + 1) - (2x + 1) '\times 4x}{ {(2x + 1)}^{2} } = \\ = \frac{4(2x + 1) - 2 \times 4x}{ {(2x + 1)}^{2} } = \\ = \frac{8x + 4 - 8x}{ {(2x + 1)}^{2} } = \frac{4}{ {(2x + 1)}^{2} }$