Question

Найти производную функции заданной неявно: y*sin x - cos(x-y) = 0

Answer 1

Ответ:

$y \sin(x) - \cos(x - y) = 0 \\ y' \sin(x) + ( \sin(x))'\times y - ( - \sin(x - y)) \times (x - y)' = 0 \\ y' \sin(x) + y \cos(x) + \sin(x - y) \times (1 - y') = 0 \\ y ' \sin(x) + y \cos(x) + \sin(x - y) - y'\sin(x - y) = 0 \\ y'( \sin(x) - \sin(x - y)) = - y \cos(x) - \sin(x - y) \\ y '= - \frac{y \cos(x) + \sin(x - y) }{ \sin(x) - \sin(x - y) }\\ y '= \frac{y \cos(x) + \sin(x - y) }{ \sin(x - y) -\sin(x)}$