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

解

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

- \frac{7}{( x - 3 ) ^{2}}

解答ステップ

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

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

\frac{d}{d x} (x - 3) = 1

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

簡素化

\frac{2 ( x - 3 ) - 1 \cdot ( 2 x + 1 )}{( x - 3 ) ^{2}} : - \frac{7}{( x - 3 ) ^{2}}

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