Question

Помогите пожалуйста найти производную
$y = ln( sqrt[3]{ sin(2x) } )$

Answer 1

$y = lnsqrt[3]{ sin2x} \ y' = frac{1}{sqrt[3]{ sin2x}} times (sqrt[3]{ sin2x})' = \ = frac{1}{sqrt[3]{ sin2x}} times {(sin2x)}^{ frac{1}{3} } )' = \ = frac{1}{sqrt[3]{ sin2x}} times frac{1}{3} {(sin2x)}^{ frac{1}{3} - 1} = \ = frac{1}{sqrt[3]{ sin2x}} times frac{1}{3} {(sin2x)}^{ - frac{2}{3}} times (sin2x)' = \ = frac{1}{sqrt[3]{ sin2x}} times frac{1}{3} {(sin2x)}^{ - frac{2}{3}} times 2cos2x = \ = frac{2}{3} cos2x timesfrac{1}{sqrt[3]{ sin2x}} times frac{1}{sqrt[3]{ {(sin2x)}^{2} }} = \ = frac{2cos2x}{3sin2x} = frac{2}{3} ctg2x$

Answer 2

Спасибо огромное

Answer 3

ok