derivative of ((x+1^3)/x)

解

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{x})

\frac{3 x ( x + 1 ) ^{2} - ( x + 1 ) ^{3}}{x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{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 + 1 ) ^{3} ) x - \frac{d x}{d x} ( x + 1 ) ^{3}}{x ^{2}}

\frac{d}{d x} ((x + 1)^{3}) = 3 (x + 1)^{2}

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

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

簡素化

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