Question

РЕШИТЕ ПОЖАЛУЙСТА ОЧЕНЬ НУЖНО 40 БАЛЛОВ ДАЮ​

Answer 1

Ответ:

1

1.

$y '= ln(12) \times {12}^{x} + 9 {x}^{2} + 30 {x}^{4} + 4 \sin(x) - \frac{4}{ x }$

2.

$y '= 36 + 4 \times \frac{1}{2} {x}^{ - \frac{1}{2} } + 4 {e}^{x} - \frac{5}{ { \cos }^{2} x} = \\ = 36 + \frac{2}{ \sqrt{x} } + 4 {e}^{x} - \frac{5}{ { \cos }^{2}x }$

3.

$y' = 60 {x}^{4} + 24 {x}^{3} - 5 + 18 {x}^{ - 7} + 0 - 12 {x}^{ - 4} = \\ = 60 {x}^{4} + 24 {x}^{3} - 5 + \frac{18}{ {x}^{7} } - \frac{12}{ {x}^{4} }$

2

1.

$y = u'v + v'u = ( {7}^{x} \times ln(7) + \frac{2}{x} - 12 {x}^{3} )(7 \sqrt{x} - 4 \cos(x) ) + \\ + ( \frac{7}{2 \sqrt{x} } + 4 \sin(x) )(12 + {7}^{x} + 2 ln(x) - 3 {x}^{4} )$

2.

$y = u'v + v'u = ( - 6 {x}^{ - 2} + \frac{1}{ { \sin}^{2}x } )(8 {x}^{9} - 3 {e}^{x} ) + (72 {x}^{8} - 3 {e}^{x} )(3 \cos(5) - \frac{6}{x} - ctgx) = \\ = ( - \frac{6}{ {x}^{2} } + \frac{1}{ { \sin}^{2} x} )(8 {x}^{9} - 3 {e}^{x} ) + (72 {x}^{8} - 3 {e}^{x} )(3 \cos(5) - \frac{6}{x} - ctgx)$

3.

$y = (4 ln(x) \times {x}^{6} ) '\cos(x) + ( \cos(x)) '(4 ln(x) \times {x}^{6} ) = \\ = ((4 ln(x))' {x}^{6} + ( {x}^{6} )'4 ln(x) ) \cos(x) - \sin(x) \times 4 {x}^{6} ln(x) = \\ = ( \frac{4}{x} \times {x}^{6} + 6 {x}^{5} \times 4 ln(x)) \cos(x) - 4{x}^{6} ln(x) \sin(x) = \\ = (4 {x}^{5} + 24 {x}^{5} ln(x)) \cos(x) - 4 {x}^{6} ln(x) \sin(x)$

3

1.

$y' = \frac{u'v - v'u}{ {v}^{2} } = \frac{( - 4 \sin(x) + 39 {x}^{ - 4} )(4x - 3 {e}^{x} - \sqrt{6}) - (4 - 3 {e}^{x})(4 \cos(x) - 13 {x}^{ - 3} - 2) }{ {(4x - 3 {e}^{x} - \sqrt{6} )}^{2} } = \\ = \frac{( - 4 \sin(x) + \frac{39}{ {x}^{4} } )(4x - 3 {e}^{x} - \sqrt{6}) - (4 - 3 {e}^{x})(4 \cos(x) - \frac{13}{ {x}^{3} } - 2) }{ {(4x - 3 {e}^{x} - \sqrt{6} )}^{2} }$

2.

$y '= \frac{(1 - 6x - {8}^{x} \times ln(8) - {e}^{x} )(9 {x}^{2} + \cos(x)) - (18x - \sin(x))(x - 3 {x}^{2} - {8}^{x} - {e}^{x} ) }{ {(9 {x}^{2} + \cos(x)) }^{2} }$

3.

$y' = \frac{( {6}^{x} \cos(x))' \times {3}^{x} - ({3}^{x}) ' \times {6}^{x} \cos(x) }{ {3}^{2x} } = \\ = \frac{( ln(6) \times {6}^{x} \cos(x) - {6}^{x} \sin(x)) \times {3}^{x} - {3}^{x} ln(3) \times {6}^{x} \cos(x) }{ {3}^{2x} } = \\ = \frac{ {3}^{x} \times {6}^{x} ( ln(6) \cos(x) - \sin(x) - ln(3) \cos(x)) }{ {3}^{2x} } = \\ = {2}^{x} ( ln(6) \cos(x) - \sin(x) - ln(3) \cos(x))$

4

1.

$y '= \frac{1}{2 \sqrt{ ln( { \sin }^{5} (8 {x}^{3} - {6}^{x} )) } } \times \frac{1}{ { \sin }^{5} (8 {x}^{3} - {6}^{x}) } \times \\ \times 5 { \sin }^{4} (8 {x}^{3} - {6}^{x} ) \times \cos(8 {x}^{3} - {6}^{x} )) \times (24 {x}^{2} - {6}^{x} ln(6)) = \\ = \frac{5(24 {x}^{2} - {6}^{x} ln(6)) \times ctg(8 {x}^{3} - {6}^{x} )}{2 \sqrt{ ln( { \sin}^{5}(8 {x}^{3} - {6}^{x} )) } }$

2.

$y '= 6 {ln}^{5} ( {e}^{ {(16 {x}^{3} + 5x)}^{ \frac{1}{3} } } ) \times \frac{1}{ {e}^{ {(16 {x}^{3} + 5x)}^{ \frac{1}{3} } }} \times {e}^{ {(16 {x}^{3} + 5x)}^{ \frac{1}{3} } } \times \\ \times \frac{1}{3} {(16 {x}^{3} + 5x)}^{ - \frac{2}{3} } \times (48 {x}^{2} + 5) = \\ = \frac{2(48 {x}^{2} + 5) {ln}^{5}( {e}^{ {(16 {x}^{3} + 5x)}^{ \frac{1}{3} } })}{ \sqrt[3]{ {(16 {x}^{3} + 5x) }^{2} } }$