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

解

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

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

解答ステップ

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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