derivative of (3-17x^2/(3x^3))

解

\frac{d}{d x} (\frac{3 - 17 x ^{2}}{3 x ^{3}})

- \frac{- 17 x ^{2} + 9}{3 x ^{4}}

解答ステップ

\frac{d}{d x} (\frac{3 - 17 x ^{2}}{3 x ^{3}})

定数を除去:

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

= \frac{1}{3} \frac{d}{d x} (\frac{3 - 17 x ^{2}}{x ^{3}})

商の法則を適用:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( 3 - 17 x ^{2} ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 - 17 x ^{2} )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 - 17 x^{2}) = - 34 x

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

= \frac{1}{3} \cdot \frac{( - 34 x ) x ^{3} - 3 x ^{2} ( 3 - 17 x ^{2} )}{( x ^{3} ) ^{2}}

簡素化

\frac{1}{3} \cdot \frac{( - 34 x ) x ^{3} - 3 x ^{2} ( 3 - 17 x ^{2} )}{( x ^{3} ) ^{2}} : - \frac{- 17 x ^{2} + 9}{3 x ^{4}}

= - \frac{- 17 x ^{2} + 9}{3 x ^{4}}