Question

Богом прошу, помогите!

Найдите производную:
1) f (x) = x^6 / 6
2) f (x) = 1 / x^2
3) f (x) = (x^2 - 1) / x
4) f (x) = ctg 3x
5*) f (x) = (x√3/3) + x^3

Answer 1

$1) f'(x) = \frac{1}{6} * x^{6} = \frac{1}{6} * 6 * x^{5} = x^{5}$
$5) f'(x) = \frac{ \sqrt{3} }{3} + 3 x^{2}$$2) f'(x) = x^{-2} =-2 * x^{-3}$
$3) f'(x) = \frac{2x * x - x^{2} + 1 }{ x^{2}} = \frac{ x^{2} + 1 }{ x^{2} }$
$4) f'(x) = - \frac{3}{ sin^{2}3x}$