derivative of x/((5x-4^3))

解

\frac{d}{d x} (\frac{x}{( 5 x - 4 ) ^{3}})

- \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}

解答ステップ

\frac{d}{d x} (\frac{x}{( 5 x - 4 ) ^{3}})

商の法則を適用:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((5 x - 4)^{3}) = 15 (5 x - 4)^{2}

= \frac{1 \cdot ( 5 x - 4 ) ^{3} - 15 ( 5 x - 4 ) ^{2} x}{( ( 5 x - 4 ) ^{3} ) ^{2}}

簡素化

\frac{1 \cdot ( 5 x - 4 ) ^{3} - 15 ( 5 x - 4 ) ^{2} x}{( ( 5 x - 4 ) ^{3} ) ^{2}} : - \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}

= - \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}