derivative of 3/((4x^2-1^4))

解

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

- \frac{96 x}{( 4 x ^{2} - 1 ) ^{5}}

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{1}{( 4 x ^{2} - 1 ) ^{4}})

指数の規則を適用する:

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

= 3 \frac{d}{d x} ((4 x^{2} - 1)^{- 4})

連鎖法則を適用:

- \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \frac{d}{d x} (4 x^{2} - 1)

= - \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \frac{d}{d x} (4 x^{2} - 1)

\frac{d}{d x} (4 x^{2} - 1) = 8 x

= 3 (- \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \cdot 8 x)

簡素化

3 (- \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \cdot 8 x) : - \frac{96 x}{( 4 x ^{2} - 1 ) ^{5}}

= - \frac{96 x}{( 4 x ^{2} - 1 ) ^{5}}