(\partial)/(\partial x)(e^z(x-y)^2)

解

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

2 e^{z} (x - y)

解答ステップ

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

z, y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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