derivative of 2-(x^2-2x+4/(x-2))

解

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

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2) = 0

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

= 0 - \frac{x ^{2} - 4 x}{( x - 2 ) ^{2}}

簡素化

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