derivative of ((2x^2-1/(1-x^2))^3)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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