(\partial)/(\partial y)(cos(x)+xcos(y)-y)

解

\frac{\partial}{\partial y} (cos (x) + x cos (y) - y)

- x sin (y) - 1

解答ステップ

\frac{\partial}{\partial y} (cos (x) + x cos (y) - y)

x

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (cos (x)) + \frac{\partial}{\partial y} (x cos (y)) - \frac{\partial}{\partial y} (y)

\frac{\partial}{\partial y} (cos (x)) = 0

\frac{\partial}{\partial y} (x cos (y)) = - x sin (y)

\frac{\partial}{\partial y} (y) = 1

= 0 - x sin (y) - 1

簡素化

= - x sin (y) - 1