What is the derivative of |x^2-2x-3| ?

The derivative of |x^2-2x-3| is ((x^2-2x-3)(2x-2))/(|x^2-2x-3|)

What is the first derivative of |x^2-2x-3| ?

The first derivative of |x^2-2x-3| is ((x^2-2x-3)(2x-2))/(|x^2-2x-3|)

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

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

Solution steps

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

Apply the chain rule:

\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)

Multiply fractions:

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)

- \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}

What is the derivative of |x^2-2x-3| ?
The derivative of |x^2-2x-3| is ((x^2-2x-3)(2x-2))/(|x^2-2x-3|)
What is the first derivative of |x^2-2x-3| ?
The first derivative of |x^2-2x-3| is ((x^2-2x-3)(2x-2))/(|x^2-2x-3|)