derivative of (-4x^5-2pi^2/(x^7))

解

\frac{d}{d x} (\frac{- 4 x ^{5} - 2 π ^{2}}{x ^{7}})

- \frac{2 ( - 4 x ^{5} - 7 π ^{2} )}{x ^{8}}

解答ステップ

\frac{d}{d x} (\frac{- 4 x ^{5} - 2 π ^{2}}{x ^{7}})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( - 4 x ^{5} - 2 π ^{2} ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ( - 4 x ^{5} - 2 π ^{2} )}{( x ^{7} ) ^{2}}

\frac{d}{d x} (- 4 x^{5} - 2 π^{2}) = - 20 x^{4}

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{( - 20 x ^{4} ) x ^{7} - 7 x ^{6} ( - 4 x ^{5} - 2 π ^{2} )}{( x ^{7} ) ^{2}}

簡素化

\frac{( - 20 x ^{4} ) x ^{7} - 7 x ^{6} ( - 4 x ^{5} - 2 π ^{2} )}{( x ^{7} ) ^{2}} : - \frac{2 ( - 4 x ^{5} - 7 π ^{2} )}{x ^{8}}

= - \frac{2 ( - 4 x ^{5} - 7 π ^{2} )}{x ^{8}}