derivative ((3t-1))/(sqrt(t)-2)

解

導関数

\frac{( 3 t - 1 )}{t - 2}

\frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{3 t - 1}{t - 2})

商の法則を適用:

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

= \frac{\frac{d}{d t} ( 3 t - 1 ) ( t - 2 ) - \frac{d}{d t} ( t - 2 ) ( 3 t - 1 )}{( t - 2 ) ^{2}}

\frac{d}{d t} (3 t - 1) = 3

\frac{d}{d t} (t - 2) = \frac{1}{2 t}

= \frac{3 ( t - 2 ) - \frac{1}{2 t} ( 3 t - 1 )}{( t - 2 ) ^{2}}

簡素化

\frac{3 ( t - 2 ) - \frac{1}{2 t} ( 3 t - 1 )}{( t - 2 ) ^{2}} : \frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}

= \frac{3 t - 12 t + 1}{2 t ( t - 2 ) ^{2}}