derivative (2x^3+8)/x

解

導関数

\frac{2 x ^{3} + 8}{x}

\frac{4 x ^{3} - 8}{x ^{2}}

解答ステップ

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

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

\frac{d x}{d x} = 1

= \frac{6 x ^{2} x - 1 \cdot ( 2 x ^{3} + 8 )}{x ^{2}}

簡素化

\frac{6 x ^{2} x - 1 \cdot ( 2 x ^{3} + 8 )}{x ^{2}} : \frac{4 x ^{3} - 8}{x ^{2}}

= \frac{4 x ^{3} - 8}{x ^{2}}