(\partial)/(\partial x)(8e^{7x-y})

解

\frac{\partial}{\partial x} (8 e^{7 x - y})

56 e^{7 x - y}

解答ステップ

\frac{\partial}{\partial x} (8 e^{7 x - y})

y

を定数として扱う

定数を除去:

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

= 8 \frac{\partial}{\partial x} (e^{7 x - y})

連鎖法則を適用:

e^{7 x - y} \frac{\partial}{\partial x} (7 x - y)

= e^{7 x - y} \frac{\partial}{\partial x} (7 x - y)

\frac{\partial}{\partial x} (7 x - y) = 7

= 8 e^{7 x - y} \cdot 7

簡素化

= 56 e^{7 x - y}