derivative of (sqrt(-x+y-2)/(x-2))

解

\frac{d}{d x} (\frac{- x + y - 2}{x - 2})

\frac{x \frac{d y}{d x} + x - 2 y - 2 \frac{d y}{d x} + 6}{2 ( x - 2 ) ^{2} - x + y - 2}

解答ステップ

\frac{d}{d x} (\frac{- x + y - 2}{x - 2})

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

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

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

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

簡素化

\frac{\frac{\frac{d y}{d x} - 1}{2 - x + y - 2} ( x - 2 ) - 1 \cdot - x + y - 2}{( x - 2 ) ^{2}} : \frac{x \frac{d y}{d x} + x - 2 y - 2 \frac{d y}{d x} + 6}{2 ( x - 2 ) ^{2} - x + y - 2}

= \frac{x \frac{d y}{d x} + x - 2 y - 2 \frac{d y}{d x} + 6}{2 ( x - 2 ) ^{2} - x + y - 2}