derivative of (x-7/(sqrt(x)-\sqrt{7)})

解

\frac{d}{d x} (\frac{x - 7}{x - 7})

\frac{x - 2 7 x + 7}{2 x ( x - 7 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x - 7}{x - 7})

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 - 7 ) ( x - 7 ) - \frac{d}{d x} ( x - 7 ) ( x - 7 )}{( x - 7 ) ^{2}}

\frac{d}{d x} (x - 7) = 1

\frac{d}{d x} (x - 7) = \frac{1}{2 x}

= \frac{1 \cdot ( x - 7 ) - \frac{1}{2 x} ( x - 7 )}{( x - 7 ) ^{2}}

簡素化

\frac{1 \cdot ( x - 7 ) - \frac{1}{2 x} ( x - 7 )}{( x - 7 ) ^{2}} : \frac{x - 2 7 x + 7}{2 x ( x - 7 ) ^{2}}

= \frac{x - 2 7 x + 7}{2 x ( x - 7 ) ^{2}}