derivative of (2x+1/(3-5x))

解

\frac{d}{d x} (\frac{2 x + 1}{3 - 5 x})

\frac{11}{( 3 - 5 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 x + 1}{3 - 5 x})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 2 x + 1 ) ( 3 - 5 x ) - \frac{d}{d x} ( 3 - 5 x ) ( 2 x + 1 )}{( 3 - 5 x ) ^{2}}

\frac{d}{d x} (2 x + 1) = 2

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

= \frac{2 ( 3 - 5 x ) - ( - 5 ) ( 2 x + 1 )}{( 3 - 5 x ) ^{2}}

簡素化

\frac{2 ( 3 - 5 x ) - ( - 5 ) ( 2 x + 1 )}{( 3 - 5 x ) ^{2}} : \frac{11}{( 3 - 5 x ) ^{2}}

= \frac{11}{( 3 - 5 x ) ^{2}}