Question

Найдите производную: cos xy = y/x

Answer 1

Ответ:

$\cos(xy) = \frac{y}{x}$

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