(\partial)/(\partial x)(9xe^{2xy})

解

\frac{\partial}{\partial x} (9 x e^{2 x y})

9 (e^{2 x y} + 2 e^{2 x y} x y)

解答ステップ

\frac{\partial}{\partial x} (9 x e^{2 x y})

y

を定数として扱う

定数を除去:

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

= 9 \frac{\partial}{\partial x} (x e^{2 x y})

積の法則を適用:

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

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

= 9 (\frac{\partial}{\partial x} (x) e^{2 x y} + \frac{\partial}{\partial x} (e^{2 x y}) x)

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

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

= 9 (1 \cdot e^{2 x y} + e^{2 x y} \cdot 2 y x)

簡素化

= 9 (e^{2 x y} + 2 e^{2 x y} x y)