Question

Помогите решить правила дифференцирования

Answer 1

Ответ:

1.

$1)y' = 6x - 4$

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

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

$4)y' = {e}^{ \sin(x) } \times \cos(x) \\ 5)y' = \frac{1}{ {x}^{6} + {x}^{4} } \times (6 {x}^{5} + 4 {x}^{3} )$

2.

$a)f'(x) = 12 {x}^{2} - 8 \\ f'(2) = 12 \times 4 - 8 = 48 - 8 = 40$

$b)f'(x) = \frac{1}{2} \times {(3x + 6)}^{ - \frac{1}{2} } \times 3 = \frac{3}{2 \sqrt{3x + 6} } \\ f'(1) = \frac{3}{2 \sqrt{3 + 6} } = \frac{3}{3 \times 2} = \frac{1}{2} = 0.5$