Question

Найти производную
$y = frac{5 sin(3x) }{6 cos(5x ) }$

С решением!!!!

Answer 1

$y = frac{5 sin(3x) }{6 cos(5x ) } \ \y = frac{u}{v} \ y' = frac{u'v - uv'}{ {v}^{2} } \ \ y' = frac{(5sin(3x))' times 6cos(5x) -5sin(3x) times (6cos(5x))'}{ {(6cos(5x))}^{2} } = \ = frac{5cos(3x) times 3 times 6cos(5x) + 5sin(3x) times 6sin(5x) times 5}{{(6cos(5x))}^{2}} = \ = frac{90cos(3x) times cos(5x) + 150sin(3x) times sin(5x)}{{36cos}^{2}(5x)}$