derivative (x^9+7)/(x^9)

解

導関数

\frac{x ^{9} + 7}{x ^{9}}

- \frac{63}{x ^{10}}

解答ステップ

\frac{d}{d x} (\frac{x ^{9} + 7}{x ^{9}})

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 ^{9} + 7 ) x ^{9} - \frac{d}{d x} ( x ^{9} ) ( x ^{9} + 7 )}{( x ^{9} ) ^{2}}

\frac{d}{d x} (x^{9} + 7) = 9 x^{8}

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{9 x ^{8} x ^{9} - 9 x ^{8} ( x ^{9} + 7 )}{( x ^{9} ) ^{2}}

簡素化

\frac{9 x ^{8} x ^{9} - 9 x ^{8} ( x ^{9} + 7 )}{( x ^{9} ) ^{2}} : - \frac{63}{x ^{10}}

= - \frac{63}{x ^{10}}