derivative h(x)=[(x+1)/(x-1)]^3

解

導関数

h (x) = [\frac{x + 1}{x - 1}]^{3}

- \frac{6 ( x + 1 ) ^{2}}{( x - 1 ) ^{4}}

解答ステップ

\frac{d}{d x} ((\frac{x + 1}{x - 1})^{3})

連鎖法則を適用:

3 (\frac{x + 1}{x - 1})^{2} \frac{d}{d x} (\frac{x + 1}{x - 1})

= 3 (\frac{x + 1}{x - 1})^{2} \frac{d}{d x} (\frac{x + 1}{x - 1})

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

= 3 (\frac{x + 1}{x - 1})^{2} (- \frac{2}{( x - 1 ) ^{2}})

簡素化

3 (\frac{x + 1}{x - 1})^{2} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{6 ( x + 1 ) ^{2}}{( x - 1 ) ^{4}}

= - \frac{6 ( x + 1 ) ^{2}}{( x - 1 ) ^{4}}