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

解

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

\frac{4 x ^{2} + 12 x + 1}{( 2 x + 3 ) ^{2}}

解答ステップ

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

\frac{d}{d x} ((x + 1) (2 x - 5)) = 4 x - 3

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

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

拡張

(4 x - 3) (2 x + 3) - 2 (x + 1) (2 x - 5) : 4 x^{2} + 12 x + 1

= \frac{4 x ^{2} + 12 x + 1}{( 2 x + 3 ) ^{2}}