derivative (x^2+6)/(5x-2)

解

導関数

\frac{x ^{2} + 6}{5 x - 2}

\frac{5 x ^{2} - 4 x - 30}{( 5 x - 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2} + 6}{5 x - 2})

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 ^{2} + 6 ) ( 5 x - 2 ) - \frac{d}{d x} ( 5 x - 2 ) ( x ^{2} + 6 )}{( 5 x - 2 ) ^{2}}

\frac{d}{d x} (x^{2} + 6) = 2 x

\frac{d}{d x} (5 x - 2) = 5

= \frac{2 x ( 5 x - 2 ) - 5 ( x ^{2} + 6 )}{( 5 x - 2 ) ^{2}}

拡張

2 x (5 x - 2) - 5 (x^{2} + 6) : 5 x^{2} - 4 x - 30

= \frac{5 x ^{2} - 4 x - 30}{( 5 x - 2 ) ^{2}}