(\partial)/(\partial y)(xe^{x^2-y})

解

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

- e^{x^{2} - y} x

解答ステップ

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

連鎖法則を適用:

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

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

\frac{\partial}{\partial y} (x^{2} - y) = - 1

= x e^{x^{2} - y} (- 1)

簡素化

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