Question

1)f(x)=x²(x²-2)
2)f(x)=x⁵+4x+tgx
3)f(x)=xcosx
Найти производную

Answer 1

1)

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

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

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

2)

$f(x) = {x}^{5} + 4x + tg(x)$

$f'(x) = 5 {x}^{4} + 4 + \frac{1}{ {cos}^{2} (x) } = \frac{5 {x}^{4} {cos}^{2}(x) + 4 {cos}^{2} (x) + 1 }{ {cos}^{2}(x) }$

3)

$f(x) = x \times \cos(x)$

$f'(x) = (x)' \times \cos(x) + x \times ( \cos(x) )'$

$f'(x) = 1 \times \cos(x) + x \times ( - \sin(x) ) = \cos(x) - x \times \sin(x)$