derivative of |x^3+8x^2+5x-50|

解

\frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

\frac{( x ^{3} + 8 x ^{2} + 5 x - 50 ) ( 3 x ^{2} + 16 x + 5 )}{∣ x ^{3} + 8 x ^{2} + 5 x - 50 ∣}

解答ステップ

\frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

連鎖法則を適用:

\frac{x ^{3} + 8 x ^{2} + 5 x - 50}{∣ ( x ^{3} + 8 x ^{2} + 5 x - 50 ) ∣} \frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

= \frac{x ^{3} + 8 x ^{2} + 5 x - 50}{∣ ( x ^{3} + 8 x ^{2} + 5 x - 50 ) ∣} \frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

\frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50) = 3 x^{2} + 16 x + 5

= \frac{x ^{3} + 8 x ^{2} + 5 x - 50}{∣ ( x ^{3} + 8 x ^{2} + 5 x - 50 ) ∣} (3 x^{2} + 16 x + 5)

分数を乗じる:

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

= \frac{( x ^{3} + 8 x ^{2} + 5 x - 50 ) ( 3 x ^{2} + 16 x + 5 )}{∣ x ^{3} + 8 x ^{2} + 5 x - 50 ∣}