derivative f(w)=((2w^4-5w))/(9w)

解

導関数

f (w) = \frac{( 2 w ^{4} - 5 w )}{9 w}

\frac{2 w ^{2}}{3}

解答ステップ

\frac{d}{d w} (\frac{2 w ^{4} - 5 w}{9 w})

定数を除去:

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

= \frac{1}{9} \frac{d}{d w} (\frac{2 w ^{4} - 5 w}{w})

商の法則を適用:

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

= \frac{1}{9} \cdot \frac{\frac{d}{d w} ( 2 w ^{4} - 5 w ) w - \frac{d w}{d w} ( 2 w ^{4} - 5 w )}{w ^{2}}

\frac{d}{d w} (2 w^{4} - 5 w) = 8 w^{3} - 5

\frac{d w}{d w} = 1

= \frac{1}{9} \cdot \frac{( 8 w ^{3} - 5 ) w - 1 \cdot ( 2 w ^{4} - 5 w )}{w ^{2}}

簡素化

\frac{1}{9} \cdot \frac{( 8 w ^{3} - 5 ) w - 1 \cdot ( 2 w ^{4} - 5 w )}{w ^{2}} : \frac{2 w ^{2}}{3}

= \frac{2 w ^{2}}{3}