(\partial)/(\partial x)(1/6 x^3)

解

\frac{\partial}{\partial x} (\frac{1}{6} x^{3})

\frac{x ^{2}}{2}

解答ステップ

\frac{\partial}{\partial x} (\frac{1}{6} x^{3})

定数を除去:

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

= \frac{1}{6} \frac{\partial}{\partial x} (x^{3})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{6} \cdot 3 x^{3 - 1}

簡素化

\frac{1}{6} \cdot 3 x^{3 - 1} : \frac{x ^{2}}{2}

= \frac{x ^{2}}{2}