derivative of (-11/(2(x-2)^2)-4/(x-2))

解

\frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}} - \frac{4}{x - 2})

\frac{4 x + 3}{( x - 2 ) ^{3}}

解答ステップ

\frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}} - \frac{4}{x - 2})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}}) - \frac{d}{d x} (\frac{4}{x - 2})

\frac{d}{d x} (\frac{- 11}{2 ( x - 2 ) ^{2}}) = \frac{11}{( x - 2 ) ^{3}}

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

= \frac{11}{( x - 2 ) ^{3}} - (- \frac{4}{( x - 2 ) ^{2}})

簡素化

\frac{11}{( x - 2 ) ^{3}} - (- \frac{4}{( x - 2 ) ^{2}}) : \frac{4 x + 3}{( x - 2 ) ^{3}}

= \frac{4 x + 3}{( x - 2 ) ^{3}}