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

解

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

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

解答ステップ

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

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

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

\frac{d}{d x} (x + 4) = 1

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

簡素化

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

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