Question

Необходимо решить, заменив N=10

Answer 1

Ответ:

$1)y = 10 + 10\pi + \sin(10) \\ y' = 0$

$2)y = \frac{ {x}^{10} }{10} + 10x + \sqrt{x} + 10$

$y' = {x}^{9 } + 10 + \frac{1}{2 \sqrt{x} }$

$3)y = \frac{1}{10 {x}^{10} } \\ y' = \frac{1}{10} \times ( - 10 {x}^{ - 11} ) = - \frac{ 1}{ {x}^{11} }$

$4)y = 10 \sqrt[10]{ {x}^{3} } \\ y' = 10 \times \frac{3}{10} {x}^{ - \frac{7}{10} } = \frac{3}{ \sqrt[10]{ {x}^{7} } }$

$5)y = \frac{12}{ \sqrt[12]{ {x}^{5} } } \\ y' = 11 \times ( - \frac{5}{12} {x}^{ - \frac{17}{12} } ) = - \frac{55}{12x \sqrt[12]{ {x}^{5} } }$

$6)y = \frac{x}{ \sqrt[13]{ {x}^{7} } } = {x}^{1 - \frac{7}{13} } = {x}^{ \frac{6}{13} } \\ y' = \frac{6}{13} {x}^{ - \frac{7}{13} } = \frac{6}{13 \sqrt[13]{ {x}^{7} } }$

$7)y = {x}^{10} ctg(x) \\ y' = 10 {x}^{9} ctg(x) - \frac{ {x}^{10} }{ { \sin(x) }^{2} }$

$8)y = \frac{10 {x}^{10} + 1 }{10 {x}^{10} - 1 }$

$y' = \frac{100 {x}^{9} (10 {x}^{10} - 1) - 100 {x}^{9} (10 {x}^{10} + 1) }{ {(10 {x}^{10} - 1) }^{2} } = \frac{ - 200 {x}^{9} }{ {(10 {x}^{10} - 1)}^{2} }$

$9)y = \frac{x}{10 - ln(x) } \\ y' = \frac{10 - ln(x) + \frac{1}{x} \times x}{ {(10 - ln(x)) }^{2} } = \frac{10 - ln(x) + 1 }{ {(10 - ln(x)) }^{2} } = \frac{11 - ln(x) }{ {(10 - ln(x)) }^{2} }$

$10)y' = 2 {e}^{x} - 3 \cos(x) - 4 \sin(x) + \frac{5}{x} - \frac{1}{ { \cos(x) }^{2} } - \frac{1}{ { \sin( {x} ) }^{2} }$