Question

Продифференцировать данные функции

Answer 1

6.

а)

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

б)

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

а)

$y' = 5 \cos(x) - \sin(x) \times (12 + 5x) - 4 \times ( - 1) {x}^{ - 2} = \\ = 5 \cos(x) - (5x + 12) \sin(x) + \frac{4}{ {x}^{2} }$

б)

$y' = ln(10) \times {10}^{ {x}^{4} + 0.5 { \sin }^{2}(7x) } \times (4 {x}^{3} + \sin(7x) \cos(7x) \times 7) = \\ = ln(10) (4 {x}^{3} + 7 \sin(7x) \cos(7x) ) \times {10}^{2 {x}^{4} + 0.5 { \sin}^{2}(7x) }$