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

解

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

- \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{3}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 2 \cdot \frac{x ^{2} + 3}{x ^{2} - 3} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

簡素化

2 \cdot \frac{x ^{2} + 3}{x ^{2} - 3} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{3}}

= - \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{3}}