derivative of (3x+4/(7x-5))

解

\frac{d}{d x} (\frac{3 x + 4}{7 x - 5})

- \frac{43}{( 7 x - 5 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{3 x + 4}{7 x - 5})

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 ) ( 7 x - 5 ) - \frac{d}{d x} ( 7 x - 5 ) ( 3 x + 4 )}{( 7 x - 5 ) ^{2}}

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

\frac{d}{d x} (7 x - 5) = 7

= \frac{3 ( 7 x - 5 ) - 7 ( 3 x + 4 )}{( 7 x - 5 ) ^{2}}

簡素化

\frac{3 ( 7 x - 5 ) - 7 ( 3 x + 4 )}{( 7 x - 5 ) ^{2}} : - \frac{43}{( 7 x - 5 ) ^{2}}

= - \frac{43}{( 7 x - 5 ) ^{2}}