derivative y=(6t-3)/(5t+8)

解

導関数

y = \frac{6 t - 3}{5 t + 8}

\frac{63}{( 5 t + 8 ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{6 t - 3}{5 t + 8})

商の法則を適用:

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

= \frac{\frac{d}{d t} ( 6 t - 3 ) ( 5 t + 8 ) - \frac{d}{d t} ( 5 t + 8 ) ( 6 t - 3 )}{( 5 t + 8 ) ^{2}}

\frac{d}{d t} (6 t - 3) = 6

\frac{d}{d t} (5 t + 8) = 5

= \frac{6 ( 5 t + 8 ) - 5 ( 6 t - 3 )}{( 5 t + 8 ) ^{2}}

拡張

6 (5 t + 8) - 5 (6 t - 3) : 63

= \frac{63}{( 5 t + 8 ) ^{2}}