derivative of (x^2/(7x+4))

解

\frac{d}{d x} (\frac{x ^{2}}{7 x + 4})

\frac{7 x ^{2} + 8 x}{( 7 x + 4 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2}}{7 x + 4})

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} ) ( 7 x + 4 ) - \frac{d}{d x} ( 7 x + 4 ) x ^{2}}{( 7 x + 4 ) ^{2}}

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

\frac{d}{d x} (7 x + 4) = 7

= \frac{2 x ( 7 x + 4 ) - 7 x ^{2}}{( 7 x + 4 ) ^{2}}

拡張

2 x (7 x + 4) - 7 x^{2} : 7 x^{2} + 8 x

= \frac{7 x ^{2} + 8 x}{( 7 x + 4 ) ^{2}}