derivative of 24x^{3/2}

解

\frac{d}{d x} (24 x^{\frac{3}{2}})

36 x^{\frac{1}{2}}

解答ステップ

\frac{d}{d x} (24 x^{\frac{3}{2}})

定数を除去:

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

= 24 \frac{d}{d x} (x^{\frac{3}{2}})

乗の法則を適用:

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

= 24 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

簡素化

24 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : 36 x^{\frac{1}{2}}

= 36 x^{\frac{1}{2}}