derivative of 3/4 x^{3/2}

解

\frac{d}{d x} (\frac{3}{4} x^{\frac{3}{2}})

\frac{9 x ^{\frac{1}{2}}}{8}

解答ステップ

\frac{d}{d x} (\frac{3}{4} x^{\frac{3}{2}})

定数を除去:

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

= \frac{3}{4} \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}

= \frac{3}{4} \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

簡素化

\frac{3}{4} \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{9 x ^{\frac{1}{2}}}{8}

= \frac{9 x ^{\frac{1}{2}}}{8}