derivative of |x^3+2x^2-4x-8|

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

分式相乘:

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

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

x \to 4 lim (3 e^{1.7 x} + 1)

y^{^{''}} - 4 y^{^{'}} + 4 y = 8 x^{2} + e^{2 x}

d er i v a t i v e y = 3 x^{3} + 45 x^{2} + 81 x

\int \frac{1}{x x + 4} d x

a re a y = sin^{2} (x), y = sin^{3} (x)