derivative of (3x-4/((5x+2)^3))

解

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

\frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

解答ステップ

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

商の法則を適用:

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

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

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

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

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

簡素化

\frac{3 ( 5 x + 2 ) ^{3} - 15 ( 5 x + 2 ) ^{2} ( 3 x - 4 )}{( ( 5 x + 2 ) ^{3} ) ^{2}} : \frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

= \frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}