(\partial)/(\partial y)(e^{xy}+2x-5y)

解

\frac{\partial}{\partial y} (e^{x y} + 2 x - 5 y)

e^{x y} x - 5

解答ステップ

\frac{\partial}{\partial y} (e^{x y} + 2 x - 5 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} (2 x) - \frac{\partial}{\partial y} (5 y)

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

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

\frac{\partial}{\partial y} (5 y) = 5

= e^{x y} x + 0 - 5

簡素化

= e^{x y} x - 5