(\partial)/(\partial x)(x^2ye^{x-z})

解

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

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

解答ステップ

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

y, z

を定数として扱う

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{x - z}

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

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

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

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