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

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

分式相乘:

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

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

x \to 2 lim (2 x^{2} + 1)

d er i v a t i v e - \frac{x + 3 arcsin ( x )}{4}

\int \frac{4 x - 10}{x ^{2} - 6 x + 8} d x

\int \frac{x + 2}{x + 5} d x

f (t) = t^{6}