Математика: Математика найти производную

Математика найти производную

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Ответ:

веселаямышка

31.12.2020 09:05

$1)y' = - 28 {x}^{6} + 3 \times \frac{3}{7} {x}^{ - \frac{4}{7} } - 4 \times 3 {x}^{ - 4} = - 28 {x}^{6} + \frac{9}{7 \sqrt[7]{ {x}^{4} } } - \frac{12}{ {x}^{4} }$

$2)y' = - \frac{1}{ \sqrt{1 - {x}^{2} } } ctg(x) - \frac{1}{ { \sin(x) }^{2} } arccos(x) = - \frac{ctg(x)}{ \sqrt{1 - {x}^{2} } } - \frac{arccos(x)}{ { \sin(x) }^{2} }$

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

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

$5)y' = ln(3) \times {3}^{arcsin(x)} \times \frac{1}{ \sqrt{1 - {x}^{2} } }$

$6)y' = {e}^{ \sin(x) + {x}^{2} } \times ( \cos(x) + 2x)$

$7)y' = \frac{1}{ \sqrt{ \frac{1 - x}{1 + x} } } \times \frac{1}{2} {( \frac{1 - x}{1 + x}) }^{ - \frac{1}{2} } \times \frac{( - 1(1 + x) - (1 - x))}{ {(1 + x)}^{2} } = \sqrt{ \frac{1 + x}{1 - x} } \times \frac{1}{2} \times \sqrt{ \frac{1 + x}{1 - x} } \times \frac{ - 1 - x - 1 + x}{ {(1 + x)}^{2} } = \frac{1}{2} \times \frac{1 + x}{1 - x} \times \frac{ - 2}{ {(1 + x)}^{2} } = - \frac{1}{(1 - x)(1 + x)} = - \frac{1 }{1 - {x}^{2} }$

$8)y' = 7 { \sin(x) }^{6} {e}^{2x} + 2 {e}^{2x} { \sin(x) }^{7} = {e}^{2x} { \sin(x) }^{6} (7 + 2 \sin(x) )$

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

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

$11)y' = 9 {(1 + \sqrt{1 - x} )}^{2} \times \frac{1}{2} {(1 - x)}^{ - \frac{1}{2} } \times ( - 1) = \frac{ - 9 {(1 + \sqrt{1 - x}) }^{2} }{2 \sqrt{1 - x} }$

$12)y' = 3 { \cos( \sqrt{ {e}^{3x} } ) }^{2} \times ( - \sin( \sqrt{ {e}^{3x} } ) ) \times \frac{3}{2} {e}^{ \frac{x}{2} } = - \frac{9}{2} \sqrt{ {e}^{x} } { \cos( \sqrt{ {e}^{3x} } ) }^{2} \sin( \sqrt{ {e}^{3x} } )$