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

解

導関数

\frac{x - 4}{x + 4}

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

解答ステップ

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

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

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

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

簡素化

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

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