derivative of (11-11x/(7x^{3/7)})

解

\frac{d}{d x} (\frac{11 - 11 x}{7 x ^{\frac{3}{7}}})

\frac{- 44 x - 33}{49 x ^{\frac{10}{7}}}

解答ステップ

\frac{d}{d x} (\frac{11 - 11 x}{7 x ^{\frac{3}{7}}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{7} \frac{d}{d x} (\frac{11 - 11 x}{x ^{\frac{3}{7}}})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{7} \cdot \frac{\frac{d}{d x} ( 11 - 11 x ) x ^{\frac{3}{7}} - \frac{d}{d x} ( x ^{\frac{3}{7}} ) ( 11 - 11 x )}{( x ^{\frac{3}{7}} ) ^{2}}

\frac{d}{d x} (11 - 11 x) = - 11

\frac{d}{d x} (x^{\frac{3}{7}}) = \frac{3}{7 x ^{\frac{4}{7}}}

= \frac{1}{7} \cdot \frac{( - 11 ) x ^{\frac{3}{7}} - \frac{3}{7 x ^{\frac{4}{7}}} ( 11 - 11 x )}{( x ^{\frac{3}{7}} ) ^{2}}

簡素化

\frac{1}{7} \cdot \frac{( - 11 ) x ^{\frac{3}{7}} - \frac{3}{7 x ^{\frac{4}{7}}} ( 11 - 11 x )}{( x ^{\frac{3}{7}} ) ^{2}} : \frac{- 44 x - 33}{49 x ^{\frac{10}{7}}}

= \frac{- 44 x - 33}{49 x ^{\frac{10}{7}}}