(\partial)/(\partial y)(e^{xy}-(x+1)cos(y))

解

\frac{\partial}{\partial y} (e^{x y} - (x + 1) cos (y))

e^{x y} x + sin (y) (x + 1)

解答ステップ

\frac{\partial}{\partial y} (e^{x y} - (x + 1) cos (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} (e^{x y}) - \frac{\partial}{\partial y} ((x + 1) cos (y))

\frac{\partial}{\partial y} (e^{x y}) = e^{x y} x

\frac{\partial}{\partial y} ((x + 1) cos (y)) = - sin (y) (x + 1)

= e^{x y} x - (- sin (y) (x + 1))

簡素化

= e^{x y} x + sin (y) (x + 1)