(\partial)/(\partial x)(ue^{2x})

解

\frac{\partial}{\partial x} (u (x) e^{2 x})

\frac{\partial}{\partial x} (u) e^{2 x} + e^{2 x} \cdot 2 u

解答ステップ

\frac{\partial}{\partial x} (u e^{2 x})

積の法則を適用:

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

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

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

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

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