Question

Вычислить Производную Функции

Answer 1

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

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

$3)y' = ( - 2 {x}^{ - \frac{7}{6} } )' = 2 \times \frac{7}{6} {x}^{ - \frac{13}{6} } = \frac{7}{3 {x}^{2} \sqrt[6]{x} }$

$4)y' = ln(7) \times {7}^{ \frac{1}{x} } \times ( - {x}^{ - 2} ) - 7 {x}^{ - 8} = - \frac{ ln(7) \times {7}^{x} }{ {x}^{2} } - \frac{7}{ {x}^{8} }$

$5)y' = \frac{1}{ { \cos(7x) }^{2} } \times 7$

$6)y' = - \sin( \frac{\pi}{4} - x) \times ( - 1) = \sin( \frac{\pi}{4} - x )$

$7)y' = 2x \times \cos( \frac{5x}{2} ) + {x}^{2} \times ( - \sin( \frac{5x}{2} ) ) \times \frac{5}{2} = 2x \cos( \frac{5x}{2} ) - \frac{5 {x}^{2} }{2} \sin( \frac{5x}{2} )$

$8)y' = \frac{3}{2} \times \frac{1}{ ln(3) \times 4x} \times 4 = \frac{3}{2x ln(3) }$

$9)y' = 7 {( {e}^{x} + 5 )}^{6} \times {e}^{x}$

$10)y' = \frac{1}{ \frac{1}{ {x}^{2} } } \times ( - 2 {x}^{ - 3} ) - 0 = \\ {x}^{2} \times ( \frac{ - 2}{ {x}^{3} } ) = - \frac{2}{x}$