(\partial)/(\partial y)(xe^{5y})

解

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

x e^{5 y} \cdot 5

解答ステップ

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

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial y} (e^{5 y})

連鎖法則を適用:

e^{5 y} \frac{\partial}{\partial y} (5 y)

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

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

= x e^{5 y} \cdot 5