Question

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

С решением!!!!

Answer 1

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