(\partial)/(\partial y)(z^2e^{xy})

解

\frac{\partial}{\partial y} (z^{2} e^{x y})

z^{2} e^{x y} x

解答ステップ

\frac{\partial}{\partial y} (z^{2} e^{x y})

z, x

を定数として扱う

定数を除去:

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

= z^{2} \frac{\partial}{\partial y} (e^{x y})

連鎖法則を適用:

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

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

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

= z^{2} e^{x y} x