Question

Вычислить производную у=cos8x/tg5x Сроооочнооо

Answer 1

$\displaystyle y= \frac{cos8x}{tg5x} = \frac{(cos(8x))'(tg(5x))-(cos(8x))(tg(5x))'}{(tg(5x)) ^2} = \\ \\ = \frac{(-8sin(8x))(tg(5x))-(cos(8x))( \frac{5}{cos(5x)^2}) }{(tg(5x))^2} \\ \\ (cos(8x))' = (cos(8x))'(8x)' = -8sin(8x) \\ \\ (8x)' = 8 \\ \\ (tg(5x))' =(tg(5x))' (5x)' = \frac{5}{cos(5x)^2} \\ \\ (5x)' = 5 \\ \\ \frac{cos(8x)}{tg(5x)^2}*(-5tg(5x)^2 -5)-8 * \frac{sin(8x)}{tg(5x)}$