Question

Помогите решить задание

Answer 1

$1) \: f(x)^{l} = (4 {e}^{x} - 5 ln(x) + \frac{3}{7} \ctg(x))^{l} = 4 {e}^{x} - \frac{5}{x} - \frac{3}{7} \times \frac{1}{ { \sin }^{2} (x)} = 4 {e}^{x} - \frac{5}{x} - \frac{3}{ { 7\sin }^{2} (x)}$
$2) \: y^{l} = (5x(2 {x}^{2} - 3x + 4))^{l} = (10 {x}^{3} - 15 {x}^{2} + 20x)^{l} = 30 {x}^{2} - 30x + 20$
$3) \: f(x)^{l} = (3 ln(2 {x}^{2} + 1 )) ^{l} = \frac{3}{2 {x}^{2} + 1} \times (2 {x}^{2} + 1)^{l} = \frac{12x}{2 {x}^{2} + 1 }$
$4) \: f(x)^{l} = ( \frac{ {x}^{2} + 4 }{3x - 1} )^{l} = \frac{( {x}^{2} + 4) ^{l} \times (3x - 1) - ( {x}^{2} + 4)(3x - 1)^{l} }{(3x - 1)^{2} } = \frac{2x(3x - 1) - 3( {x}^{2} + 4) }{(3x - 1)^{2}} = \frac{6 {x}^{2} - 2x - 3 {x}^{2} - 12 }{(3x - 1)^{2}} = \frac{3 {x}^{2} - 2x - 12}{(3x - 1)^{2}}$