derivative of |x^4-4x^2|

解

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

\frac{( x ^{4} - 4 x ^{2} ) ( 4 x ^{3} - 8 x )}{∣ x ^{4} - 4 x ^{2} ∣}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{4} - 4 x^{2}) = 4 x^{3} - 8 x

= \frac{x ^{4} - 4 x ^{2}}{∣ ( x ^{4} - 4 x ^{2} ) ∣} (4 x^{3} - 8 x)

分数を乗じる:

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

= \frac{( x ^{4} - 4 x ^{2} ) ( 4 x ^{3} - 8 x )}{∣ x ^{4} - 4 x ^{2} ∣}