Question

Полностью расписать похідну функцію ​

Answer 1

Ответ:

1

$f'(x) = (2 {x}^{3} \sqrt{x} ) '= (2 {x}^{3 + \frac{1}{2} } )' = (2 {x}^{ \frac{7}{2} } ) '= \\ = 2 \times \frac{7}{2} {x}^{ \frac{5}{2} } = 7 {x}^{2} \sqrt{x}$

2

$f'(x) = ( {x}^{2} \cos(x) ) '= ( {x}^{2} )' \cos(x) + ( \cos(x)) ' \times {x}^{2} = \\ = 2x \cos(x) - \sin(x) \times {x}^{2} = \\ = 2x \cos(x) - {x}^{2} \sin(x)$

3

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