Question

Найти неявную производную y^2 + 5x = sin(y+x)

Answer 1

Ответ:

${y}^{2} + 5x = \sin(x + y) \\ 2y \times y' + 5 = \cos(x + y) \times (1 + y') \\ 2y'y + 5 = \cos(x + y) + y'\cos(x + y) \\ 2y'y - y' \cos(x + y) = - 5 + \cos(x + y) \\ y'(2y - \cos(x + y)) = \cos(x + y) - 5 \\ y' = \frac{2y - \cos(x + y) }{ \cos(x + y) - 5 }$