derivative of (5x+2/(sqrt(x+1)))

解

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

\frac{5 x + 8}{2 ( x + 1 ) x + 1}

解答ステップ

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

商の法則を適用:

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

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

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

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

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

簡素化

\frac{5 x + 1 - \frac{1}{2 x + 1} ( 5 x + 2 )}{( x + 1 ) ^{2}} : \frac{5 x + 8}{2 ( x + 1 ) x + 1}

= \frac{5 x + 8}{2 ( x + 1 ) x + 1}