Question

помогите, умоляю
сложные производные функции​

Answer 1

Ответ:

2.

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

3.

$y' = \frac{1}{ \sqrt{1 - {9x}^{2} } } \times 3 - \frac{1}{2} {(1 - 9 {x}^{2} )}^{ - \frac{1}{2} } \times ( - 18x) = \\ = \frac{3}{ \sqrt{1 - 9 {x}^{2} } } + \frac{3x}{ \sqrt{1 - 9 {x}^{2} } } = \frac{3x + 3}{ \sqrt{1 - 9 {x}^{2} } }$

4.

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

5.

$y '= \frac{( \sin(5x)) ' \times (1 - 2 \sin(5x)) - (1 - 2\sin(5x))' \times \sin(5x) }{ {(1 - 2 \sin(5x)) }^{2} } = \\ = \frac{5 \cos(5x)(1 - 2 \sin(2x)) + 10 \cos(5x) \times \sin(5x) }{ {(1 - 2 \sin(5x)) }^{2} } = \\ = \frac{5 \cos(5x) - 10 \sin(5x) \cos(5x) + 10\sin(5x) \cos(5x) }{ {(1 - 2 \sin(5x)) }^{2} } = \\ = \frac{5 \cos(5x) }{ {(1 - 2 \sin(5x)) }^{2} }$