(\partial)/(\partial y)(cos(x)cos(y)+2x)

解

\frac{\partial}{\partial y} (cos (x) cos (y) + 2 x)

- cos (x) sin (y)

解答ステップ

\frac{\partial}{\partial y} (cos (x) cos (y) + 2 x)

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) cos (y)) + \frac{\partial}{\partial y} (2 x)

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

\frac{\partial}{\partial y} (2 x) = 0

= - cos (x) sin (y) + 0

簡素化

= - cos (x) sin (y)