derivative of |x^3+10x^2+25x|

解

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\frac{( x ^{3} + 10 x ^{2} + 25 x ) ( 3 x ^{2} + 20 x + 25 )}{∣ x ^{3} + 10 x ^{2} + 25 x ∣}

解答ステップ

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

連鎖法則を適用:

\frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} \frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

= \frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} \frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x) = 3 x^{2} + 20 x + 25

= \frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} (3 x^{2} + 20 x + 25)

分数を乗じる:

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

= \frac{( x ^{3} + 10 x ^{2} + 25 x ) ( 3 x ^{2} + 20 x + 25 )}{∣ x ^{3} + 10 x ^{2} + 25 x ∣}