derivative f(x)=(x^2)/(3+8x)

解

導関数

f (x) = \frac{x ^{2}}{3 + 8 x}

\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2}}{3 + 8 x})

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 + 8 x ) - \frac{d}{d x} ( 3 + 8 x ) x ^{2}}{( 3 + 8 x ) ^{2}}

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

\frac{d}{d x} (3 + 8 x) = 8

= \frac{2 x ( 3 + 8 x ) - 8 x ^{2}}{( 3 + 8 x ) ^{2}}

拡張

2 x (3 + 8 x) - 8 x^{2} : 6 x + 8 x^{2}

= \frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}