(\partial)/(\partial x)(e^{(x+y)}-1)

解

\frac{\partial}{\partial x} (e^{(x + y)} - 1)

e^{x + y}

解答ステップ

\frac{\partial}{\partial x} (e^{(x + y)} - 1)

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (1) = 0

= e^{x + y} - 0

簡素化

= e^{x + y}