(\partial)/(\partial x)(-2e^{4y-x^2-y^2}x)

解

\frac{\partial}{\partial x} (- 2 e^{4 y - x^{2} - y^{2}} x)

- 2 (- 2 e^{4 y - x^{2} - y^{2}} x^{2} + e^{4 y - x^{2} - y^{2}})

解答ステップ

\frac{\partial}{\partial x} (- 2 e^{4 y - x^{2} - y^{2}} x)

y

を定数として扱う

定数を除去:

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

= - 2 \frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}} x)

積の法則を適用:

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

f = e^{4 y - x^{2} - y^{2}}, g = x

= - 2 (\frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}}) x + \frac{\partial}{\partial x} (x) e^{4 y - x^{2} - y^{2}})

\frac{\partial}{\partial x} (e^{4 y - x^{2} - y^{2}}) = - 2 e^{4 y - x^{2} - y^{2}} x

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

= - 2 ((- 2 e^{4 y - x^{2} - y^{2}} x) x + 1 \cdot e^{4 y - x^{2} - y^{2}})

簡素化

- 2 ((- 2 e^{4 y - x^{2} - y^{2}} x) x + 1 \cdot e^{4 y - x^{2} - y^{2}}) : - 2 (- 2 e^{4 y - x^{2} - y^{2}} x^{2} + e^{4 y - x^{2} - y^{2}})

= - 2 (- 2 e^{4 y - x^{2} - y^{2}} x^{2} + e^{4 y - x^{2} - y^{2}})