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

解答

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

\frac{( x ^{3} + 3 x ^{2} - 8 ) ( 3 x ^{2} + 6 x )}{∣ x ^{3} + 3 x ^{2} - 8 ∣}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (x^{3} + 3 x^{2} - 8) = 3 x^{2} + 6 x

= \frac{x ^{3} + 3 x ^{2} - 8}{∣ ( x ^{3} + 3 x ^{2} - 8 ) ∣} (3 x^{2} + 6 x)

分式相乘:

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

= \frac{( x ^{3} + 3 x ^{2} - 8 ) ( 3 x ^{2} + 6 x )}{∣ x ^{3} + 3 x ^{2} - 8 ∣}

\int 3 cos^{3} (2 x) d x

ma c l a u r in e^{x} cos (x)

\frac{d}{d t} (2)

d er i v a t i v e f (x) = (- 9 x^{3} + 2 x^{2})^{5}

\int e^{x} \cdot 2 d x