(\partial)/(\partial x)((z)(x^2e^y+10y))

解

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} + 10 y))

2 e^{y} z x

解答ステップ

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} + 10 y))

z, y

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial x} (x^{2} e^{y} + 10 y)

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (x^{2} e^{y}) + \frac{\partial}{\partial x} (10 y))

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

\frac{\partial}{\partial x} (10 y) = 0

= z (2 e^{y} x + 0)

簡素化

= 2 e^{y} z x