derivative (x^2)/(3x+7)

解

導関数

\frac{x ^{2}}{3 x + 7}

\frac{3 x ^{2} + 14 x}{( 3 x + 7 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2}}{3 x + 7})

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} ) ( 3 x + 7 ) - \frac{d}{d x} ( 3 x + 7 ) x ^{2}}{( 3 x + 7 ) ^{2}}

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

\frac{d}{d x} (3 x + 7) = 3

= \frac{2 x ( 3 x + 7 ) - 3 x ^{2}}{( 3 x + 7 ) ^{2}}

拡張

2 x (3 x + 7) - 3 x^{2} : 3 x^{2} + 14 x

= \frac{3 x ^{2} + 14 x}{( 3 x + 7 ) ^{2}}