Question

Найти функцию производной y=tg6x / на корень sin X

Answer 1

Ответ:

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

Пошаговое объяснение:

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

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

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