(\partial)/(\partial x)(xe^{4x})

解

\frac{\partial}{\partial x} (x e^{4 x})

e^{4 x} + 4 e^{4 x} x

解答ステップ

\frac{\partial}{\partial x} (x e^{4 x})

積の法則を適用:

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

f = x, g = e^{4 x}

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

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

\frac{\partial}{\partial x} (e^{4 x}) = e^{4 x} \cdot 4

= 1 \cdot e^{4 x} + e^{4 x} \cdot 4 x

簡素化

= e^{4 x} + 4 e^{4 x} x