(\partial)/(\partial x)(8xe^{5xy})

解

\frac{\partial}{\partial x} (8 x e^{5 x y})

8 (e^{5 x y} + 5 e^{5 x y} x y)

解答ステップ

\frac{\partial}{\partial x} (8 x e^{5 x y})

y

を定数として扱う

定数を除去:

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

= 8 \frac{\partial}{\partial x} (x e^{5 x y})

積の法則を適用:

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

f = x, g = e^{5 x y}

= 8 (\frac{\partial}{\partial x} (x) e^{5 x y} + \frac{\partial}{\partial x} (e^{5 x y}) x)

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

\frac{\partial}{\partial x} (e^{5 x y}) = e^{5 x y} \cdot 5 y

= 8 (1 \cdot e^{5 x y} + e^{5 x y} \cdot 5 y x)

簡素化

= 8 (e^{5 x y} + 5 e^{5 x y} x y)