Question

Найдите производную функции:
1)f(x)=8x^5 -3x^2 +4
2)f(x)=(3-4x)sqrt x
3)f(x)=x^2 -2/x

Answer 1

Ответ:

1

$f(x) = 8 {x}^{5} - 3 {x}^{2} + 4$

$f'(x) = 8 \times 5 {x}^{4} - 3 \times 2x + 0 = \\ = 40 {x}^{4} - 6x$

2

$f(x) = ((3 - 4x) \sqrt{x} ) '= (3 \sqrt{x} - 4x \sqrt{x} )' = \\ = (3 {x}^{ \frac{1}{2} } - 4 {x}^{ \frac{3}{2} } ) '= 3 \times \frac{1}{2} {x}^{ - \frac{1}{2} } - 4 \times \frac{3}{2} {x}^{ \frac{1}{2} } = \\ = \frac{3}{2 \sqrt{x} } - 6 \sqrt{x}$

3

$f(x) = \frac{ {x}^{2} - 2}{x}$

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