derivative of (x^{3/2}+2/x)

解

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

\frac{x ^{\frac{3}{2}} - 4}{2 x ^{2}}

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x^{\frac{3}{2}} + 2) = \frac{3 x ^{\frac{1}{2}}}{2}

\frac{d x}{d x} = 1

= \frac{\frac{3 x ^{\frac{1}{2}}}{2} x - 1 \cdot ( x ^{\frac{3}{2}} + 2 )}{x ^{2}}

簡素化

\frac{\frac{3 x ^{\frac{1}{2}}}{2} x - 1 \cdot ( x ^{\frac{3}{2}} + 2 )}{x ^{2}} : \frac{x ^{\frac{3}{2}} - 4}{2 x ^{2}}

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