derivative of (x+1/(x^5))

解

\frac{d}{d x} (\frac{x + 1}{x ^{5}})

\frac{- 4 x - 5}{x ^{6}}

解答ステップ

\frac{d}{d x} (\frac{x + 1}{x ^{5}})

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 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( x + 1 )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (x + 1) = 1

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1 \cdot x ^{5} - 5 x ^{4} ( x + 1 )}{( x ^{5} ) ^{2}}

簡素化

\frac{1 \cdot x ^{5} - 5 x ^{4} ( x + 1 )}{( x ^{5} ) ^{2}} : \frac{- 4 x - 5}{x ^{6}}

= \frac{- 4 x - 5}{x ^{6}}