derivative y=|x^2-8|

解

導関数

y = x^{2} - 8

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

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

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