derivative of (x-11/(sqrt(x)-\sqrt{11)})

解

\frac{d}{d x} (\frac{x - 11}{x - 11})

\frac{x - 2 11 x + 11}{2 x ( x - 11 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x - 11}{x - 11})

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 - 11 ) ( x - 11 ) - \frac{d}{d x} ( x - 11 ) ( x - 11 )}{( x - 11 ) ^{2}}

\frac{d}{d x} (x - 11) = 1

\frac{d}{d x} (x - 11) = \frac{1}{2 x}

= \frac{1 \cdot ( x - 11 ) - \frac{1}{2 x} ( x - 11 )}{( x - 11 ) ^{2}}

簡素化

\frac{1 \cdot ( x - 11 ) - \frac{1}{2 x} ( x - 11 )}{( x - 11 ) ^{2}} : \frac{x - 2 11 x + 11}{2 x ( x - 11 ) ^{2}}

= \frac{x - 2 11 x + 11}{2 x ( x - 11 ) ^{2}}