derivative y=(3(x-1))/(4xsqrt(x))

解

導関数

y = \frac{3 ( x - 1 )}{4 x x}

\frac{3 ( - x + 3 )}{8 x ^{\frac{5}{2}}}

解答ステップ

\frac{d}{d x} (\frac{3 ( x - 1 )}{4 x x})

定数を除去:

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

= \frac{3}{4} \frac{d}{d x} (\frac{x - 1}{x x})

商の法則を適用:

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

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

\frac{d}{d x} (x - 1) = 1

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

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

簡素化

\frac{3}{4} \cdot \frac{1 \cdot x x - \frac{3 x}{2} ( x - 1 )}{( x x ) ^{2}} : \frac{3 ( - x + 3 )}{8 x ^{\frac{5}{2}}}

= \frac{3 ( - x + 3 )}{8 x ^{\frac{5}{2}}}