Question

Найдите производные функций
ХЕЛП ПЛИИИИЗ

Answer 1

Ответ:

а)

$f'(x) =5 \times 3 {(3x + {x}^{3} - 4 {x}^{4}) }^{2} \times (3x + {x}^{3} - 4 {x}^{4} )' = \\ = 15 {(3x + {x}^{3} - 4 {x}^{4} )}^{2} \times (3 + 3 {x}^{2} - 16 {x}^{3} ) = \\ = 15(3 + 3 {x}^{2} - 16 {x}^{3} ) {(3x + {x}^{3} - 4 {x}^{4}) }^{2}$

б)

$f'(x) = 2 \times (4 {x}^{2} - {x}^{4} ) \times (4 {x}^{2} - {x}^{4} )' = \\ = 2(4 {x}^{2} - {x}^{4 }) \times (8x - 4 {x}^{3} )$

в)

$f'(x) = 5 {(3 \sqrt{x} - 2 {x}^{2} + {x}^{5} ) }^{4} \times (3 \times \frac{1}{2} {x}^{ - \frac{1}{2} } - 4x + 5 {x}^{4} ) = \\ = 5 {(3 \sqrt{x} - 2 {x}^{2} + {x}^{5}) }^{4} ( \frac{3}{2 \sqrt{x} } - 4x + 5 {x}^{4} )$

г)

$f'(x) = 5 {(4 \sqrt{x} + 6 {x}^{2} - 5x)}^{4} \times (4 \times \frac{1}{2} {x}^{ - \frac{1}{2} } + 12x - 5) = \\ = 5 {(4 \sqrt{x} + 6 {x}^{2} - 5x)}^{4} \times ( \frac{2}{ \sqrt{x} } + 12x - 5)$