Question

Найти функцию производной y=tg6x / на корень sin X

Answer 1

Ответ:

$frac{12sin(x) - cos(6x) * sin(6x) * cos(x)}{2sqrt{sin(x)} * cos(6x)^{2} * sin(x) }$

Пошаговое объяснение:

f(x) = $frac{tan(6x)}{sqrt{sin(x)} }$ = $tan(6x) * (sin(x))^{-frac{1}{2} }$

f'(x) = $(tan(6x))' * (sin(x))^{frac{-1}{2} } + tan(6x) * ((sin(x))^{frac{-1}{2} } )'$ =

= $frac{1}{cos^{2}(6x) } * 6 * sin^{-frac{1}{2} } (x) - tan(6x) * frac{1}{2}sin^{-frac{3}{2} } (x) *cos(x)$ = $frac{12sin(x) - cos(6x) * sin(6x) * cos(x)}{2sqrt{sin(x)} * cos(6x)^{2} * sin(x) }$