derivative of |x^3-3x^2+2|

解

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

\frac{( x ^{3} - 3 x ^{2} + 2 ) ( 3 x ^{2} - 6 x )}{∣ x ^{3} - 3 x ^{2} + 2 ∣}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{3} - 3 x^{2} + 2) = 3 x^{2} - 6 x

= \frac{x ^{3} - 3 x ^{2} + 2}{∣ ( x ^{3} - 3 x ^{2} + 2 ) ∣} (3 x^{2} - 6 x)

分数を乗じる:

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

= \frac{( x ^{3} - 3 x ^{2} + 2 ) ( 3 x ^{2} - 6 x )}{∣ x ^{3} - 3 x ^{2} + 2 ∣}