derivative of (4x+9/(sqrt(x)))

解

\frac{d}{d x} (\frac{4 x + 9}{x})

\frac{4 x - 9}{2 x x}

解答ステップ

\frac{d}{d x} (\frac{4 x + 9}{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} ( 4 x + 9 ) x - \frac{d}{d x} ( x ) ( 4 x + 9 )}{( x ) ^{2}}

\frac{d}{d x} (4 x + 9) = 4

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

= \frac{4 x - \frac{1}{2 x} ( 4 x + 9 )}{( x ) ^{2}}

簡素化

\frac{4 x - \frac{1}{2 x} ( 4 x + 9 )}{( x ) ^{2}} : \frac{4 x - 9}{2 x x}

= \frac{4 x - 9}{2 x x}